tag:blogger.com,1999:blog-7788781157359925862024-03-12T20:53:35.240-03:00Cálculohercules fontanahttp://www.blogger.com/profile/08624991926677457192noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-778878115735992586.post-53840487052792140422013-11-07T20:02:00.000-02:002013-11-07T20:02:15.704-02:00Calcul' Art<div class="separator" style="clear: both; text-align: center;">
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<b><a href="http://calculo-hpf.blogspot.com/">VOLTAR</a></b></div>
hercules fontanahttp://www.blogger.com/profile/08624991926677457192noreply@blogger.com0tag:blogger.com,1999:blog-778878115735992586.post-10611452037733512013-11-07T19:59:00.003-02:002013-11-12T17:05:59.807-02:00Integral-2<div class="separator" style="clear: both; text-align: center;">
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<b style="text-align: center;"> <a href="http://calculo-hpf.blogspot.com/">VOLTAR</a></b><br />
<br />hercules fontanahttp://www.blogger.com/profile/08624991926677457192noreply@blogger.com0tag:blogger.com,1999:blog-778878115735992586.post-75699454683648886172013-10-23T23:16:00.000-02:002013-10-24T16:30:46.781-02:00Integral-3<div class="MsoNormal">
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<a href="http://calculo-hpf.blogspot.com/">VOLTAR</a></div>
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hercules fontanahttp://www.blogger.com/profile/08624991926677457192noreply@blogger.com0tag:blogger.com,1999:blog-778878115735992586.post-89175227398038246102013-09-17T21:43:00.002-03:002013-10-13T18:32:13.760-03:00Funções-2<h3>
</h3>
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<b><span style="font-size: 18pt;">Estudo das Funções:<o:p></o:p></span></b><br />
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<b><span style="font-family: inherit; font-size: large;">O estudo das funções resulta no gráfico completo da mesma. </span></b><br />
<b><span style="font-family: inherit; font-size: large;"><br /></span></b>
<b><span style="font-family: inherit; font-size: large;">Para
funções polinomiais:<o:p></o:p></span></b></div>
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<!--[if !supportLists]--><span style="font-family: inherit; font-size: large;"><b>a)<span style="font-weight: normal;"> </span></b><b style="text-indent: -18pt;">As raízes (valores de ‘x’ para y = 0).</b></span></div>
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<!--[if !supportLists]--><span style="font-family: inherit; font-size: large;"><b>b)<span style="font-weight: normal;"> </span></b><b style="text-indent: -18pt;">Estudo da descontinuidade e cálculo das assíntotas.</b></span></div>
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<!--[if !supportLists]--><span style="font-family: inherit; font-size: large;"><b>c)<span style="font-weight: normal;"> </span></b><b style="text-indent: -18pt;">Pontos extremos (máximos e mínimos).</b></span></div>
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<!--[if !supportLists]--><span style="font-family: inherit; font-size: large;"><b>d)<span style="font-weight: normal;"> </span></b><b style="text-indent: -18pt;">Análise da continuidade.</b></span></div>
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<!--[if !supportLists]--><span style="font-family: inherit; font-size: large;"><b>e)<span style="font-weight: normal;"> </span></b><!--[endif]--></span><b><span style="font-family: inherit; font-size: large;">Traço definitivo do gráfico. </span><span style="font-size: medium;"><o:p></o:p></span></b></div>
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<b><span style="font-size: 18pt;">Assíntotas</span></b><b><span style="font-size: 18pt;"><o:p></o:p></span></b></div>
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<b><span style="font-size: 14pt;">Assíntotas são retas situadas nos limites das funções descontínuas
quando estas vão ao infinito. Podem ser horizontais ou verticais.</span></b><b><span style="font-size: 14pt;"><o:p></o:p></span></b></div>
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<b><span style="font-size: 14pt;">a) Se o valor de x = a leva a função ao infinito, temos que x = a
é uma assíntota vertical. </span></b><b><span style="font-size: 14pt;"><o:p></o:p></span></b></div>
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<b><span style="font-size: 14pt;">b) Se o valor de x infinito leva a função a um limite finito b,
temos que y = b é uma assíntota horizontal. </span></b><b><span style="font-size: 14pt;"><o:p></o:p></span></b><br />
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<b><span style="font-size: 14pt;">a) Veja os pontos de descontinuidade, e ache o limite para este
valor de ‘x’. Se limite de f(x) para x=a, for infinito, x=a é uma assíntota
vertical. No exemplo x=-1.</span></b></div>
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<b><span style="font-size: 14pt;">b) Se limite de f(x) para x infinito for b, y = b é uma assíntota
horizontal. No exemplo y = 0.</span></b><b><span style="font-size: 14pt;"><o:p></o:p></span></b></div>
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<b><span style="font-size: 14pt;">c) Na prática, se f(x) = g(x) / h(x).<o:p></o:p></span></b></div>
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<b><span style="font-size: 14pt;">Faça h(x) = 0, e ache as raízes. Teste as raízes em g(x), se não der
0, elas são assíntotas verticais, porque uma divisão por 0 é ∞, e ‘y’ será ∞. <o:p></o:p></span></b></div>
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<b><span style="font-size: 14pt;">No exemplo: h(x)= x<sup>2</sup>-1=0 onde x= ±1. Teste em g(x) +1 não serve, -1 serve, e é uma assíntota
vertical.<o:p></o:p></span></b><br />
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<b><span style="font-size: 18pt;">Máximos e Mínimos</span></b><br />
<b><span style="font-size: 14pt;"> </span></b><br />
<b><span style="font-size: 14pt;"> Uma função não monótona varia mudando a direção, e apresenta pontos de máximos, mínimos e de inflexão. Nestes pontos os valores de 'x' são chamados de extremantes, que podem ser maximizantes ou minimizantes, e os valores de 'y' são chamados extremos.</span></b><br />
<b><span style="font-size: 14pt;"> Uma função pode ter vários pontos extremos, sendo o maior de todos chamado de máximo maximorum e o menor de mínimo minimorum.</span></b><br />
<b><span style="font-size: 14pt;"> Assim a função muda de direção, cresce ou decresce. Diz-se que ela cresce, quando os valores de 'y' crescem com os de 'x'. No estudo da função deve se analisar os intervalos em que ela cresce ou decresce, como também os pontos em que ela se torna descontínua.</span></b></div>
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<b><span style="font-size: 18pt;"> </span></b></div>
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<b><span style="font-size: large;">Como achar os pontos de máximos, mínimos e inflexão?</span></b></div>
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<b><span style="font-size: 14pt;">1- Ache a derivada primeira f '(x) e a segunda f ''(x) da função.</span></b><b><span style="font-size: 14pt;"><o:p></o:p></span></b></div>
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<b><span style="font-size: 14pt;">2- Ache as raízes (x<sub>1,<span class="apple-converted-space"> </span></sub>x<sub>2</sub></span></b><b><span style="font-size: 14pt;">...) de f ’(x). Estes são pontos de máximo ou
mínimo. Se não forem encontradas raízes a função pode não ter extremos, então
analise a continuidade da função para confirmar.<o:p></o:p></span></b></div>
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<b><span style="font-size: 14pt;">3- Calcule os valores de f ''(x) para as raízes encontradas f ''(x<sub>1</sub>),
f ''(x<sub>2</sub>), ...</span></b><b><span style="font-size: 14pt;"><o:p></o:p></span></b></div>
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<b><span style="font-size: 14pt;">Se: f ''(x<sub>1</sub>)
> 0, x<sub>1 </sub>será um
MÍNIMO</span></b><b><span style="font-size: 14pt;"><o:p></o:p></span></b></div>
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<b><span style="font-size: 14pt;"> f ''(x<sub>1</sub>)
< 0, x<sub>1 </sub>será um
MÁXIMO</span></b><b><span style="font-size: 14pt;"><o:p></o:p></span></b></div>
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<b><span style="font-size: 14pt;"> f ''(x<sub>1</sub>)
= 0, x<sub>1 </sub>será um ponto de
indeterminação.<o:p></o:p></span></b></div>
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<b><span style="font-size: 14pt;">Então calcule f '''(x''), e proceda da mesma forma, até f <sup>n</sup>.
Calcule f <sup>n</sup>(x<sub>n-1</sub>),
sendo x<sub>n-</sub>1 a raiz de f <sup>n</sup>(x) que se estuda.<o:p></o:p></span></b></div>
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<a href="http://www.blogger.com/blogger.g?blogID=778878115735992586" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a><a href="http://www.blogger.com/blogger.g?blogID=778878115735992586" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a><a href="http://www.blogger.com/blogger.g?blogID=778878115735992586" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a><b><span style="font-size: 14pt;"> a ) Se 'n'
for par.</span></b><b><span style="font-size: 14pt;"><o:p></o:p></span></b></div>
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<b><span style="font-size: 14pt;"> Se f <sup>n</sup>(x<sub>n-1</sub>) > 0
será um MÍNIMO.</span></b><b><span style="font-size: 14pt;"><o:p></o:p></span></b></div>
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<a href="http://www.blogger.com/blogger.g?blogID=778878115735992586" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a><a href="http://www.blogger.com/blogger.g?blogID=778878115735992586" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a><a href="http://www.blogger.com/blogger.g?blogID=778878115735992586" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a><b><span style="font-size: 14pt;"> Se f <sup>n</sup>(x<sub>n-1</sub>) < 0
será um MÁXIMO.</span></b><b><span style="font-size: 14pt;"><o:p></o:p></span></b></div>
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<b><span style="font-size: 14pt;"> b) Se 'n'
for ímpar.</span></b><b><span style="font-size: 14pt;"><o:p></o:p></span></b></div>
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<b><span style="font-size: 14pt;"> Se f <sup>n</sup>(x<sub>n-1</sub>) ≠ 0,
será um ponto de inflexão.</span></b><b><span style="font-size: 14pt;"><o:p></o:p></span></b></div>
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<b><span style="font-size: 14pt;"> Se f <sup>n</sup>(x<sub>n-1</sub>) = 0, não
tem extremos nem ponto de inflexão.</span></b><b><span style="font-size: 14pt;"><o:p></o:p></span></b></div>
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<b><span style="font-size: 14pt;">4- Analise a continuidade da função e sua concavidade.</span></b><b><span style="font-size: 14pt;"><o:p></o:p></span></b></div>
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<b><span style="font-size: 14pt;"> Se f <sup>n</sup>(x<sub>n-1</sub>)
> 0 concavidade para cima , será um MÍNIMO.</span></b><b><span style="font-size: 14pt;"><o:p></o:p></span></b></div>
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<b><span style="font-size: 14pt;"> Se f <sup>n</sup>(x<sub>n-1</sub>)
< 0, concavidade para baixo, será um MÁXIMO.</span></b><b><span style="font-size: 14pt;"><o:p></o:p></span></b><br />
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<b><span style="font-size: 18pt;">Exercícios A:</span></b><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgAv_iujmgFjTFBf80Niv855CHnPDVvvqoIJkrY7rn1jsBQsdUgG_Q3-L8Q8OhQ1mG56Pqbj4RpHVwQolCAr1VlV7IQNLkjvfz6vzafWTbe-_R2I2hfS-Tbmg1Xugk4EY9wutJlui0jbw/s1600/f2ex20.jpg" imageanchor="1" style="clear: left; display: inline !important; margin-bottom: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgAv_iujmgFjTFBf80Niv855CHnPDVvvqoIJkrY7rn1jsBQsdUgG_Q3-L8Q8OhQ1mG56Pqbj4RpHVwQolCAr1VlV7IQNLkjvfz6vzafWTbe-_R2I2hfS-Tbmg1Xugk4EY9wutJlui0jbw/s1600/f2ex20.jpg" /></a><br />
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<b><span style="font-size: 18pt;">Exercícios B:</span></b><br />
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<b><span style="font-size: 14pt;">Estudar as funções: ache as raízes, as assíntotas, os
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<b><span style="font-size: 18pt;">Exercícios C:</span></b><b><span style="font-size: 18pt;"><o:p></o:p></span></b><br />
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<b style="text-align: start;"><span style="font-size: 18pt;">Exercícios D:</span></b></div>
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hercules fontanahttp://www.blogger.com/profile/08624991926677457192noreply@blogger.com0tag:blogger.com,1999:blog-778878115735992586.post-71852092500111841612013-09-11T10:58:00.001-03:002013-11-07T19:03:45.987-02:00Funções-1<div class="MsoNormal" style="margin-left: 1.0cm;">
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<b><span style="font-size: 20.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">F-1 - Definições, Gráficos e Apresentação<o:p></o:p></span></b></div>
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<b><span style="font-size: large; line-height: 115%;">F-2 – Assíntotas </span></b><b><span style="font-size: large; line-height: 115%;">(após estudo de
limites)</span></b></div>
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<span style="font-size: large;"> </span><b><span style="font-size: large; line-height: 115%;">Máximos e
mínimos</span></b><b><span style="font-size: large; line-height: 115%;"> (após estudo de
derivadas)</span></b></div>
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________________________________________________________________</div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></b>
<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></b><b><span style="line-height: 115%;"><span style="font-size: large;">a) Definições:</span><span style="font-size: medium;"><o:p></o:p></span></span></b></div>
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<!--[if !supportLists]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">1)<span style="font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Álgebra – Ramo da matemática que estuda
operações com termo desconhecido, normalmente chamado de incógnita, e que é
representado pela letra ‘x’.<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></b></div>
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<!--[if !supportLists]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">2)<span style="font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Expressão algébrica– Nome dado a uma
seqüência de operações aritméticas contendo pelo menos uma incógnita.
Dependendo da quantidade de termos as expressões podem ser chamadas de
monômios, binômios, trinômios e polinômios. </span></b><br />
<b style="text-indent: -18pt;"><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> Ex:
2x, 4- 2x, x<sup>2</sup> – 5x + 6</span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></b></div>
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<!--[if !supportLists]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">3)<span style="font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Equações – Nome dado a uma expressão
algébrica em que há uma igualdade. Neste caso haverá duas incógnitas, que
passarão a ser chamadas de variáveis. Uma independente outra dependente,
normalmente representadas pelas letras ‘x’, a independente, e ‘y’, a
dependente. </span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Ex: y = 2x, y = 4- 2x, y = x<sup>2</sup> – 5x + 6</span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></b></div>
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<!--[if !supportLists]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">4)<span style="font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Grau da expressão – É o valor do maior
grau entre os termos da expressão.<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></b></div>
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<!--[if !supportLists]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">5)<span style="font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Função – Nome especial dado às equações,
simples ou complexas, quando se quer estudá-las, e sua representação é f(x) ou
y = f(x), que querem dizer função de ‘x’ ou ‘y’ é uma função de ‘x’, ou que o
valor de ‘y’ depende do valor de ‘x’.<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></b></div>
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<!--[if !supportLists]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">6)<span style="font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Intervalo de uma função – é o conjunto de
valores de ‘y’ compreendidos entre dois valores de ‘x’ dados, que são os
extremos do intervalo. <o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">O intervalo é numérico, mas normalmente é representado pelas
letras ‘a’ e ‘b’. O intervalo será finito se seus extremos forem valores
finitos, e infinito se um deles for infinito.<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></b></div>
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<!--[if !supportLists]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">7)<span style="font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Os intervalos podem ser: <o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> a) aberto a </span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">< </span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">x </span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">< </span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">b , (a,b)
ou a - b<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> b) fechado a </span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">≤ </span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">x </span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">≤ </span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">b [a,b]
ou a /-/ b<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> c) aberto à esquerda fechado à direita </span></b><br />
<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> a </span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">< </span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">x </span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">≤ </span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">b
(a,b] ou a </span></b><b><span style="font-family: "Cambria Math","serif"; font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">⊣</span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> b<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> d) aberto à d</span></b><br />
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">ireita fechado à esquerda </span></b><br />
<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> a </span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">≤ </span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">x </span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">< </span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">b
[a,b) ou a </span></b><b><span style="font-family: "Cambria Math","serif"; font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">⊢ </span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">b<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"><br /></span></b></div>
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<!--[if !supportLists]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">8)<span style="font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Domínio de uma variável são os valores
que a variável (x) pode assumir resultando num valor válido para a função (y). Por
ex: inteiro, positivo, real, negativo. Também pode se dizer que o domínio é a
projeção da curva da função no eixo ‘x’, e imagem é a projeção no eixo ‘y’.<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></b></div>
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<!--[if !supportLists]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">9)<span style="font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Função contínua num intervalo é aquela
que sempre há um valor correspondente para ‘y’ para todo valor de ‘x’ num
intervalo.<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></b></div>
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<!--[if !supportLists]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">10<span style="font-size: 7pt; font-weight: normal; line-height: normal;"> </span></span></b><!--[endif]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Descontinuidade
de uma função ocorre quando para um valor de ‘x’,’y’ é infinito. <o:p></o:p></span></b><br />
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<b style="text-indent: -18pt;"><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">11<span style="font-size: 7pt; font-weight: normal; line-height: normal;"> </span></span></b><b style="text-indent: -18pt;"><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Função
convergente – é aquela que mesmo descontínua os valores de ‘y’ voltam a ser
reais com o mesmo sinal. A divergente não volta a ter valores de ‘y’, e se
volta tem sinal contrário.</span></b></div>
</div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></b></div>
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<!--[if !supportLists]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">12<span style="font-size: 7pt; font-weight: normal; line-height: normal;"> </span></span></b><!--[endif]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Função
unívoca é a que para cada valor de ‘x’ corresponde um único valor de ‘y’.<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></b></div>
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<!--[if !supportLists]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">13<span style="font-size: 7pt; font-weight: normal; line-height: normal;"> </span></span></b><!--[endif]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Função
algébrica é aquela que são as que podem ser expressas em de forma implícita.
Aqueles que não podem são as transcendentes (exponenciais, logarítmicas,
trigonométricas)<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></b></div>
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<!--[if !supportLists]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">14<span style="font-size: 7pt; font-weight: normal; line-height: normal;"> </span></span></b><!--[endif]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Função
par f(- x) = f(x), e ímpar f(- x) = - f(x).<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></b></div>
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<!--[if !supportLists]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">15<span style="font-size: 7pt; font-weight: normal; line-height: normal;"> </span></span></b><!--[endif]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Função
explícita é quando as variáveis ‘x’ e ‘y’ estão em termos separados na
expressão, enquanto na implícita elas aparecem no mesmo termo. </span></b><br />
<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> Ex y = f(x) y = 2x+1 ou f(x,y) = 0 2xy = 6</span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></b></div>
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<!--[if !supportLists]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">16<span style="font-size: 7pt; font-weight: normal; line-height: normal;"> </span></span></b><!--[endif]--><span style="font-size: 14pt; line-height: 115%;"><b>Função
inversa é aquela que representa a operação inversa da outra, e os valores de
‘x’ de uma são os de ‘y’ da outra. ex: y = x</b><sup style="font-weight: bold;">2</sup><b> sua inversa é y </b>=</span><span style="font-size: 14pt;">√<b>x</b></span><b style="text-indent: -18pt;"><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">.</span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></b></div>
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<!--[if !supportLists]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">17<span style="font-size: 7pt; font-weight: normal; line-height: normal;"> </span></span></b><!--[endif]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Valor
numérico da função é o valor de ‘y‘ calculado a partir do valor de ‘x’. </span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Ex: f(x)= x<sup>2</sup> f(3) = 9</span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></b></div>
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<!--[if !supportLists]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">18<span style="font-size: 7pt; font-weight: normal; line-height: normal;"> </span></span></b><!--[endif]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Zeros
(raízes) da função é o valor de‘x’ para o qual y=0.<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></b></div>
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<!--[if !supportLists]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">19<span style="font-size: 7pt; font-weight: normal; line-height: normal;"> </span></span></b><!--[endif]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">O
estudo de uma função compreende: <o:p></o:p></span></b></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 7.1pt; mso-add-space: auto;">
<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">O
gráfico / As raízes / Os máximos, mínimos e pontos de inflexões / As assíntotas
/ O domínio / O limites / A derivada / A integral<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></b></div>
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<b><span style="line-height: 115%;"><span style="font-size: large;">b) Gráfico de uma Função</span><span style="font-size: medium;"><o:p></o:p></span></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">O gráfico de uma função
é a representação de todos, ou parte dos pontos da função no plano cartesiano,
polar ou vetorial. <o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><br /></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Como desenhar o gráfico?<o:p></o:p></span></b></div>
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<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Determine valores para ‘x’, aplique à
equação da função e calcule ‘y’.<o:p></o:p></span></b></div>
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<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Para funções simples faça x= </span></b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">-1<b>,
0 e 1.Para mais complexas insira outros valores.<o:p></o:p></b></span></div>
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<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Plote os pares (x,y)<o:p></o:p></span></b></div>
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função y = 2x<sup>2</sup>+3<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> </span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> </span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-no-proof: yes;"><v:shapetype coordsize="21600,21600" filled="f" id="_x0000_t75" o:preferrelative="t" o:spt="75" path="m@4@5l@4@11@9@11@9@5xe" stroked="f"><v:stroke joinstyle="miter"><v:formulas><v:f eqn="if lineDrawn pixelLineWidth 0"><v:f eqn="sum @0 1 0"><v:f eqn="sum 0 0 @1"><v:f eqn="prod @2 1 2"><v:f eqn="prod @3 21600 pixelWidth"><v:f eqn="prod @3 21600 pixelHeight"><v:f eqn="sum @0 0 1"><v:f eqn="prod @6 1 2"><v:f eqn="prod @7 21600 pixelWidth"><v:f eqn="sum @8 21600 0"><v:f eqn="prod @7 21600 pixelHeight"><v:f eqn="sum @10 21600 0"></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:formulas><v:path gradientshapeok="t" o:connecttype="rect" o:extrusionok="f"><o:lock aspectratio="t" v:ext="edit"></o:lock></v:path></v:stroke></v:shapetype><v:shape id="Imagem_x0020_1" o:spid="_x0000_i1025" style="height: 198.75pt; mso-wrap-style: square; visibility: visible; width: 334.5pt;" type="#_x0000_t75"><v:imagedata o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image001.png"></v:imagedata></v:shape></span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><o:p></o:p></span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> </span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">1) Reta (Função Linear): y = ax+b (equação do 1ºgrau)<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">2) Funções Algébricas Polinomiais: y = x</span></b><b><span style="font-size: 14pt; line-height: 21px;"><sup>n</sup></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">3) Funções transcendentes: Exponenciais y= a<sup>x </sup></span></b><b><span style="font-size: 14pt; line-height: 21px;">, y= e<sup>x</sup></span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><sup> </sup></span></b></div>
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<b><span style="font-size: 14pt; line-height: 21px;">OBS: 1) Se a = 1 ou a </span></b><b><span style="font-size: 14pt; line-height: 21px;">≤ </span></b><b><span style="font-size: 14pt; line-height: 21px;">0 não são exponenciais</span></b><b><span style="font-size: 14pt; line-height: 21px;"> </span></b><b><span style="font-size: 14pt; line-height: 21px;"> </span></b><br />
<b><span style="font-size: 14pt; line-height: 21px;"> 2) Se a = e tem um tratamento especial como y = e<sup>x</sup></span></b></div>
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<b><span style="font-size: 14pt; line-height: 21px;"><sup><br /></sup></span></b></div>
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<b><span style="font-size: 14pt; line-height: 21px;">Funções transcendentes: Logarítmicas </span></b><b><span style="font-size: 14.0pt; line-height: 115%;"> y= log<sub>a</sub> x, y= ln x</span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%;">(inversa da
exponencial)<o:p></o:p></span></b><br />
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<b><span style="font-size: 14pt; line-height: 21px;">OBS:</span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%;"> 1) Se a = 1
ou a </span></b><b><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman";">≤ </span></b><b><span style="font-size: 14.0pt; line-height: 115%;">0 não são logarítmicas</span></b><b><span style="font-size: 14.0pt; line-height: 115%;"> </span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%;"> 2) Se
a = e tem um tratamento especial
como y = ln x<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%;"> 3) Se
a = 10 tem um tratamento especial
como y = log x<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%;">Logarítmo </span></b><b><span style="font-size: 14pt; line-height: 21px;">base</span></b><br />
<b><span style="font-size: 14.0pt; line-height: 115%;">a = 10
decimal ou comum (log)<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%;">a = e
logaritmo neperiano ou natural
(ln) (e = 2,718)<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%;">a = 2
logaritmo binário<o:p></o:p></span></b><br />
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<b><span style="font-size: 14.0pt; line-height: 115%;">4) Funções Circulares ou
Trigonométricas:<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%;"> Seno,
co-seno, tangente, co-tangente, secante, co-secante<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%;"> </span></b><b><span lang="EN-US" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: EN-US;">Simbologia: y=sen x, y=cos x, y=tg x, y=cotg x, y=sec x, y=cosec x<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">Função<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">domínio<o:p></o:p></span></b></div>
</td>
<td colspan="2" style="border-left: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 77.95pt;" valign="top" width="104"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">valor
<o:p></o:p></span></b></div>
</td>
<td colspan="2" style="border-left: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 99.25pt;" valign="top" width="132"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">Limite
lateral<o:p></o:p></span></b></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-alt: solid black .5pt; mso-border-right-themecolor: text1; mso-border-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 3.0cm;" valign="top" width="113"><div class="MsoNormal">
<br /></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-left-themecolor: text1; mso-border-right-alt: solid black .5pt; mso-border-right-themecolor: text1; mso-border-right-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 134.65pt;" valign="top" width="180"><div class="MsoNormal">
<br /></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 42.5pt;" valign="top" width="57"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">x
=<o:p></o:p></span></b></div>
</td>
<td style="border-left: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 35.45pt;" valign="top" width="47"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">y
=<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 56.75pt;" valign="top" width="76"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">x→<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 42.5pt;" valign="top" width="57"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">y
=<o:p></o:p></span></b></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 3.0cm;" valign="top" width="113"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">Seno<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 134.65pt;" valign="top" width="180"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">0-90ºcresce
(+)<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">90-180º
decresce(+)<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">180-270º
decresce(-)<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">270-360º
cresce(-)<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 42.5pt;" valign="top" width="57"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">0
<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">90º<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">180º
<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">270º
<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 35.45pt;" valign="top" width="47"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">0<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">1<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">0<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">-1<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 56.75pt;" valign="top" width="76"><div class="MsoNormal">
<br /></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 42.5pt;" valign="top" width="57"><div class="MsoNormal">
<br /></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 3.0cm;" valign="top" width="113"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">Cosseno<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 134.65pt;" valign="top" width="180"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">0-90ºdecresce
(+)<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">90-180º
decresce(-)<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">180-270º
cresce(-)<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">270-360º
cresce(+)<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 42.5pt;" valign="top" width="57"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">0º
<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">90º
<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">180º
<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">270º
<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 35.45pt;" valign="top" width="47"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">1<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">0<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">-1<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">0<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 56.75pt;" valign="top" width="76"><div class="MsoNormal">
<br /></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 42.5pt;" valign="top" width="57"><div class="MsoNormal">
<br /></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 3.0cm;" valign="top" width="113"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">tangente<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 134.65pt;" valign="top" width="180"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">0-90ºcresce
(+)<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">90-180º
cresce(-)<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">180-270º
cresce(+)<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">270-360º
cresce(-)<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 42.5pt;" valign="top" width="57"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">0º
<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">90º
<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">180º
<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">270º<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 35.45pt;" valign="top" width="47"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">0<o:p></o:p></span></b></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">0<o:p></o:p></span></b></div>
<div class="MsoNormal">
<br /></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 56.75pt;" valign="top" width="76"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">90º
-<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">90º+<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">270º
-<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">270º
+<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 42.5pt;" valign="top" width="57"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">+∞<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">-
∞<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">+∞<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">-
∞<o:p></o:p></span></b></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 3.0cm;" valign="top" width="113"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">Cotangente<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 134.65pt;" valign="top" width="180"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">0-90ºdecresce
(+) <o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">90-180º
decresce(-)<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">180-270º
decresce(+)<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">270-360º
decresce(-)<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 42.5pt;" valign="top" width="57"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">0º
<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">90º
<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">180º
<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">270º<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 35.45pt;" valign="top" width="47"><div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">0<o:p></o:p></span></b></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">0<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 56.75pt;" valign="top" width="76"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">0+<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">180º
-<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">180º+<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">0
-<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 42.5pt;" valign="top" width="57"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">+∞<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">-
∞<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">+∞<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">-
∞<o:p></o:p></span></b></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 3.0cm;" valign="top" width="113"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">Secante
<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 134.65pt;" valign="top" width="180"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">0-90ºcresce
(+) <o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">90-180º
cresce(-)<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">180-270º
decresce(-)<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">270-360º
decresce(-)<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 42.5pt;" valign="top" width="57"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">0º
<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">90º
<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">180º
<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">270º<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 35.45pt;" valign="top" width="47"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">1<o:p></o:p></span></b></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">-1<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 56.75pt;" valign="top" width="76"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">90º
-<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">90º
+<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">270º
-<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">270º
+<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 42.5pt;" valign="top" width="57"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">+∞<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">-
∞<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">-∞<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">+∞<o:p></o:p></span></b></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 3.0cm;" valign="top" width="113"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">cossecante<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 134.65pt;" valign="top" width="180"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">0-90ºdecresce
(+) <o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">90-180º
cresce(+)<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">180-270º
cresce(-)<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">270-360º
decresce(-)<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 42.5pt;" valign="top" width="57"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">0º
<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">90º
<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">180º
<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">270º<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 35.45pt;" valign="top" width="47"><div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">1<o:p></o:p></span></b></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">-1<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 56.75pt;" valign="top" width="76"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">0+<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">0-<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">180º+<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">180º
-<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0cm 5.4pt 0cm 5.4pt; width: 42.5pt;" valign="top" width="57"><div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">+∞<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">-∞<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">-
∞<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; mso-bidi-font-family: "Times New Roman";">+
∞<o:p></o:p></span></b></div>
</td>
</tr>
</tbody></table>
<br />
<div class="MsoNormal">
<br /></div>
</div>
<div class="MsoNormal">
<b><span lang="EN-US" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: EN-US;"><br /></span></b></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; line-height: 115%;">5) Funções ciclométricas (inversas das
circulares)<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; line-height: 115%;"> arco
seno, arco cosseno, arco tangente, arco cotangente, arco secante, arco cossecante<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; line-height: 115%;"> Simbologia:
y=arcsen x, y=arccos x, y=arctgx, y=arccotgx, y=arcsecx, y=arccosecx<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-size: 14.0pt; line-height: 115%;"> </span></b><b><span lang="EN-US" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: EN-US;">ou: y=sen<sup>-1</sup>x,
y=cos<sup>-1</sup>x, y=tg<sup>-1</sup>x, y=cotg<sup>-1</sup>x, y=sec<sup>-1</sup>x, y=cosec<sup>-1</sup>x<o:p></o:p></span></b><br />
<b><span lang="EN-US" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: EN-US;"><br /></span></b>
<b><span lang="EN-US" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: EN-US;"><br /></span></b></div>
<div class="MsoNormal">
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<div class="MsoNormal">
<b><span lang="EN-US" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: EN-US;"><br /></span></b></div>
<div class="MsoNormal">
<div class="separator" style="clear: both; text-align: center;">
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<b><span lang="EN-US" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: EN-US;"><br /></span></b>
<b><span lang="EN-US" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: EN-US;"><br /></span></b>
<b><span style="font-size: 14.0pt; line-height: 115%;">6) Funções Hiperbólicas</span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%;"> Seno,
cosseno, tangente, cotangente, secante, cossecante (hiperbólico)<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%;"> </span></b><b><span lang="EN-US" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: EN-US;">Simbologia: y=senh x, y=cosh x, y=tgh x, y=cotgh x, y=sech x, y=cosech x<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%;"> </span></b><b><span lang="EN-US" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: EN-US;">inversas: </span></b><b><span lang="EN-US" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: EN-US;"> y=arcsenh x, y=arccosh x, y=arctgh x, y=arccotgh x, y=arcsech x, y=arccosech x</span></b></div>
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<b><span lang="EN-US" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: EN-US;"> ou: y=senh<sup>-1</sup> x, y=cosh<sup>-1</sup> x, y=tgh<sup>-1</sup> x, y=cotgh<sup>-1</sup> x, y=sech<sup>-1</sup> x, y=cosech<sup>-1</sup> x<o:p></o:p></span></b><br />
<b><span lang="EN-US" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: EN-US;"><br /></span></b>
<b><span lang="EN-US" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: EN-US;"><br /></span></b>
<b><span lang="EN-US" style="font-size: 14.0pt; line-height: 115%; mso-ansi-language: EN-US;">Fórmulas exponenciais das funções hiperbólicas:</span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%;">7) Funções Quadráticas ou Cônicas são:<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%;"> Parábola, Hipérbole, Elipse e Círculo<o:p></o:p></span></b></div>
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</h4>
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<span style="font-size: large; font-weight: bold;">8) Curvas Clássicas (em coordenadas polares)</span><br />
<span style="font-size: large; font-weight: bold;"><br /></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: 16pt;">Limaçon </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: 16pt;">ou</span><span style="font-size: 16pt;"> Caracol de Pascal</span><span style="font-size: 16pt;"><o:p></o:p></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: 14pt;">É uma </span><span style="color: windowtext; font-size: 14.0pt;"><a href="http://pt.wikipedia.org/wiki/Circunfer%C3%AAncia" title="Circunferência"><span style="color: windowtext; mso-bidi-font-family: Arial; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; text-decoration: none; text-underline: none;">circunferência</span></a> </span><span style="font-size: 14pt;">que passa
pelo polo</span><span style="font-size: 14pt;"><o:p></o:p></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: 14pt;">Equação polar: r = a </span><span style="font-size: 14pt;">± </span><span style="font-size: 14pt;">b.cos</span>θ<span style="font-size: 14pt;"> ou r =
a </span><span style="font-size: 14pt;">± </span><span style="font-size: 14pt;">b.sen</span>θ<span style="font-size: 14pt;">.<o:p></o:p></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: 14pt;"> A
equação com cos</span>θ <span style="font-size: 14pt;">é simétrica em relação ao eixo polar
cos</span>θ<span style="font-size: 14pt;">,</span>
<span style="font-size: 14pt;">e a equação com sen</span>θ<span style="font-size: 14pt;">, é simétrica em relação ao eixo normal.<o:p></o:p></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: 14pt;"> </span><span style="font-size: 14pt;">A
Limaçon pode apresentar-se com laço (a<b), sem laço (a=b neste caso é
chamada Cardióide) e convexa (a>b).<o:p></o:p></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: 16pt;">Cardióide<o:p></o:p></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: 14pt;">É
um caso particular de Limaçon (quando a = b) ou um Epiciclóide com uma ponta.
Seu aspecto é de um coração, e por isso tem este nome. <o:p></o:p></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: 16pt;">Rosácea<o:p></o:p></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: 14pt;"> Equação polar: r = a cos (n</span>θ<span style="font-size: 14pt;">) ou r = a sen(n</span>θ<span style="font-size: 14pt;">). <o:p></o:p></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: 14pt;">Se ‘n’ for par a rosácea terá 2n
pétalas; se for ímpar ela terá n pétalas.<o:p></o:p></span></div>
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<br /></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: 16pt;">Lemniscata de Bernoulli<o:p></o:p></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: 14pt;"> Equação polar: r<sup>2</sup>
= a<sup>2</sup> cos2</span>θ<span style="font-size: 14pt;"> </span><span style="font-size: 14pt;"> ou r<sup>2</sup>
= a<sup>2</sup> sen2</span><b>θ</b><span style="font-size: 14pt;">,</span>
<span style="font-size: 14pt;">para </span><span style="font-size: 14pt;"> a </span><span style="font-size: 14pt;">≠ </span><span style="font-size: 14pt;">0.<o:p></o:p></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: 14pt;">Se a > 0, cos2</span><b>θ</b><span style="font-size: 14pt;"> ou sen2</span><b>θ</b><span style="font-size: 14pt;"> devem ser > 0. Se a < 0, devem
ser < 0.<o:p></o:p></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: 14pt;">Equação
geral: 2a<sup>2</sup> = (x<sup>2</sup>+
y<sup>2</sup>)/(x<sup>2</sup>–y<sup>2</sup>)<o:p></o:p></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: 14pt;">Equação
paramétrica: x = a cos</span><span style="font-size: 14pt;">t </span><!--[if gte msEquation 12]><m:oMath><m:rad><m:radPr><m:degHide
m:val="on"/><span style='font-size:14.0pt;mso-ansi-font-size:14.0pt;
mso-bidi-font-size:14.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
Arial;color:black;font-weight:bold;font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><b><i
style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family:
"Cambria Math","serif";mso-bidi-font-family:Arial;color:black'><m:r><m:rPr><m:scr
m:val="roman"/><m:sty m:val="bi"/></m:rPr>2cos2</m:r><m:r><m:rPr><m:scr
m:val="roman"/><m:sty m:val="bi"/></m:rPr>t</m:r></span></i></b></m:e></m:rad></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-bidi-font-size: 11.0pt; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-text-raise: -5.5pt; mso-themecolor: text1; mso-themetint: 242; position: relative; top: 5.5pt;"><v:shapetype coordsize="21600,21600" filled="f" id="_x0000_t75" o:preferrelative="t" o:spt="75" path="m@4@5l@4@11@9@11@9@5xe" stroked="f">
<v:stroke joinstyle="miter">
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0">
<v:f eqn="sum @0 1 0">
<v:f eqn="sum 0 0 @1">
<v:f eqn="prod @2 1 2">
<v:f eqn="prod @3 21600 pixelWidth">
<v:f eqn="prod @3 21600 pixelHeight">
<v:f eqn="sum @0 0 1">
<v:f eqn="prod @6 1 2">
<v:f eqn="prod @7 21600 pixelWidth">
<v:f eqn="sum @8 21600 0">
<v:f eqn="prod @7 21600 pixelHeight">
<v:f eqn="sum @10 21600 0">
</v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:formulas>
<v:path gradientshapeok="t" o:connecttype="rect" o:extrusionok="f">
<o:lock aspectratio="t" v:ext="edit">
</o:lock></v:path></v:stroke></v:shapetype><v:shape id="_x0000_i1025" style="height: 21pt; width: 54pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image001.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="font-size: 14pt;"> e y =
a sent </span><!--[if gte msEquation 12]><m:oMath><m:rad><m:radPr><m:degHide
m:val="on"/><span style='font-size:14.0pt;mso-ansi-font-size:14.0pt;
mso-bidi-font-size:14.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:
Arial;color:black;font-weight:bold;font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><b><i
style='mso-bidi-font-style:normal'><span style='font-size:14.0pt;font-family:
"Cambria Math","serif";mso-bidi-font-family:Arial;color:black'><m:r><m:rPr><m:scr
m:val="roman"/><m:sty m:val="bi"/></m:rPr>2cos2</m:r><m:r><m:rPr><m:scr
m:val="roman"/><m:sty m:val="bi"/></m:rPr>t</m:r></span></i></b></m:e></m:rad></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-bidi-font-size: 11.0pt; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-text-raise: -5.5pt; mso-themecolor: text1; mso-themetint: 242; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 21pt; width: 54pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image001.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="font-size: 14pt;"><o:p></o:p></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: 14pt;"><b>Quando for co-seno, sua aparência é de um 8 deitado, e passou a significar ‘infinito’. O seno aparenta um 8 normal.</b><o:p></o:p></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: 16pt;">Espiral de Arquimedes<o:p></o:p></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: 14pt;"> Equação polar: r = b+</span><span style="font-size: 14pt;">a</span><span style="font-size: 19px;">.</span><b>θ</b><span style="font-size: 14pt;">,
sendo </span><b>θ</b><<span style="font-size: 14pt;">0 </span><span style="font-size: 14pt;">para o sentido horário</span>.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif; font-size: 14pt;"></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: 14pt;"> Espiral logarítmica: r = (e)</span><sup><span style="font-size: 18pt;">a</span></sup><sup><span style="font-size: 18pt;">θ</span></sup><span style="font-size: 14pt;"><o:p></o:p></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
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<span style="font-size: 16pt;"><span style="font-family: Arial, Helvetica, sans-serif;">Ciclóide</span><span style="font-family: Arial Rounded MT Bold, sans-serif;"><o:p></o:p></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: 14pt;">É a curva definida por um ponto de uma
circunferência que rola sobre uma reta.<o:p></o:p></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: 14pt;"> Equação polar: r<sup><b>2</b></sup> = a cos2</span><b>θ</b><span style="font-size: 14pt;">
ou r<sup><b>2</b></sup> = a sen2</span><b>θ</b></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: 14pt;"> Equação paramétrica x = r(</span><b>θ</b><span style="font-size: 14pt;">–</span><span style="font-size: 14pt;"> sen</span><b>θ</b><span style="font-size: 14pt;">)
e y = r (</span><b>θ</b><span style="font-size: 14pt;"> – cos</span><b>θ</b><span style="font-size: 14pt;">)<o:p></o:p></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: 14pt;">Tipos: curta, normal e longa.<o:p></o:p></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: 14pt;">Quando o ponto de referência está no
interior do círculo,gera a curta, e quando esta fora dele, numa extensão do
raio, gera a longa.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div class="MsoNormal">
<span style="font-size: 16pt;"><span style="font-family: Arial, Helvetica, sans-serif;">Hipociclóide</span><span style="font-family: Arial Rounded MT Bold, sans-serif;"><o:p></o:p></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: 14pt;">É a curva definida por um ponto de uma
circunferência que rola no interior de um círculo. A mais conhecidas é a
Astróide, ou hipociclóide de 4 cúspides.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: 14pt;"> Equação
polar: x = (a-b)cos</span><b>θ</b><span style="font-size: 14pt;">+b cos((a-b)</span><b>θ</b><span style="font-size: 14pt;">/b)
e <o:p></o:p></span></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: 14pt;"> </span><span lang="EN-US" style="font-size: 14pt;">y = (a-b)sen</span><b>θ</b><span lang="EN-US" style="font-size: 14pt;">+b sen((a-b)</span><b>θ</b><span lang="EN-US" style="font-size: 14pt;">/b)<o:p></o:p></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US" style="font-size: 14pt;"> </span><span style="font-size: 14pt;">Equação polar da Astóide: x
= a sen<sup>3</sup></span><b>θ</b><span style="font-size: 14pt;"> e y = a cos<sup>3</sup></span><b>θ</b><o:p></o:p></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: 16pt;">Epicicloide<o:p></o:p></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: 14pt;">É a curva definida por um ponto de uma
circunferência que rola por fora de um círculo. Pode ser normal e encurtada, e pode
haver epiciclóides evoluta e involuta. Se a = b ela
passa a ser uma cardióide.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: 14pt;"> Equação
polar: x = (a+b)cos</span><b>θ</b> <span style="font-size: 14pt;">– </span><span style="font-size: 14pt;">b cos((a+b)</span><b>θ</b><span style="font-size: 14pt;">/b)
e <o:p></o:p></span></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: 14pt;"> </span><span lang="EN-US" style="font-size: 14pt;">y = (a+b)sen</span><b>θ</b> <span lang="EN-US" style="font-size: 14pt;">– </span><span lang="EN-US" style="font-size: 14pt;">b sen((a+b)</span><b>θ</b><span lang="EN-US" style="font-size: 14pt;">/b)<o:p></o:p></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b><span lang="EN-US" style="font-size: 14pt; line-height: 21px;">c)<span style="font-size: 7pt; font-weight: normal; line-height: normal;"> </span></span></b><b><span lang="EN-US" style="font-size: 14pt; line-height: 21px;">Apresentação:</span></b></span></div>
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<b style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US" style="font-size: 14pt; line-height: 21px;"><br /></span></b><span style="font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US" style="font-size: 14pt; line-height: 21px;">1) </span></span><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: 14pt; line-height: 21px;">As equações das funções podem ser apresentadas nas formas:</span></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: 14pt; font-weight: normal; line-height: 21px;">geral ex: reta Ax + By + C=0 ou y = ax + b<o:p></o:p></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: 14pt; font-weight: normal; line-height: 21px;">normal ex: reta x cosw + y senw – p= 0<o:p></o:p></span></div>
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<span style="font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 14pt; line-height: 21px;">paramétrica ex: reta x = x<sub>o</sub>+ t cos a <o:p></o:p></span><span style="font-family: Arial, Helvetica, sans-serif; font-size: 14pt; line-height: 21px;"> y = y<sub>o</sub>+ t cos b</span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: 14pt; font-weight: normal; line-height: 21px;"> <o:p></o:p></span></div>
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<span style="font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: 14pt; line-height: 21px;">simétrica ex: reta </span></span><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: 14pt; line-height: 21px;">(x-x<sub>o</sub>)/ cos a = (y-y<sub>o</sub>)/ cos b</span></span></span></div>
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<!--[if !supportLists]--><span style="line-height: 115%;"><span style="font-size: medium;"><b> </b> </span><span style="font-family: Arial, Helvetica, sans-serif;"><b> 2)<span style="line-height: normal;"> </span></b></span></span><!--[endif]--><span style="line-height: 115%;"><span style="font-family: Arial, Helvetica, sans-serif;"><b>Coordenadas
polares:</b></span><b><o:p></o:p></b></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAQ0OqfMqXQCwWwTenV9KGC40uPIgL6JKU1MC1M2Iksi1H1sAGUcMqW6LDNzyfjRqCNfiSbd3KlP9oOdhLMXIRV59W5dUIR3UJjBKYjNm1gUxevm6e5zCc-4sgqY5cla1aRIcAOhCS2w/s1600/polar.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAQ0OqfMqXQCwWwTenV9KGC40uPIgL6JKU1MC1M2Iksi1H1sAGUcMqW6LDNzyfjRqCNfiSbd3KlP9oOdhLMXIRV59W5dUIR3UJjBKYjNm1gUxevm6e5zCc-4sgqY5cla1aRIcAOhCS2w/s1600/polar.JPG" /></a></div>
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<span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"><br /></span>
<span style="font-size: 14.0pt; line-height: 115%;"><span style="font-family: Arial, Helvetica, sans-serif;"><b>Mudança de coordenadas cartesianas e
polares:<o:p></o:p></b></span></span></div>
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<span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"><span style="font-family: Arial, Helvetica, sans-serif;"><b>Equações
transformadoras: <o:p></o:p></b></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">x =
r cos</span><!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:
normal'><span style='mso-bidi-font-size:12.0pt;line-height:115%;font-family:
"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"><o:p></o:p></span></b></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">y =
r sen</span><!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:
normal'><span style='mso-bidi-font-size:12.0pt;line-height:115%;font-family:
"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><o:p></o:p></span></b></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">tg</span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='mso-bidi-font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"> = y/x<o:p></o:p></span></b></span></div>
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<b style="font-family: Arial, Helvetica, sans-serif; line-height: 18px;">r<sup>2</sup> = x<sup>2</sup> + y<sup>2</sup></b><b style="font-family: Arial, Helvetica, sans-serif; line-height: 115%;"> </b></div>
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<br /></div>
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<span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"><span style="font-family: Arial, Helvetica, sans-serif;"><b> Exemplos:<o:p></o:p></b></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">1-
Transformar r<sup>2</sup>= 4sen2</span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='mso-bidi-font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"> para coordenadas cartesianas.<o:p></o:p></span></b></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"> sen 2</span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='mso-bidi-font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"> = 2sen</span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='mso-bidi-font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"> cos</span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='mso-bidi-font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">,
então na figura </span><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">sen 2</span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='mso-bidi-font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"> = 2(y/r)(x/r). <o:p></o:p></span></b></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"> r<sup>2</sup> = x<sup>2</sup> + y<sup>2</sup> Subst em r<sup>2</sup>= 4sen2</span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='mso-bidi-font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">, temos: (x<sup>2</sup>+y<sup>2</sup>)
= 4.2(y/r)(x/r) <o:p></o:p></span></b></span></div>
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<span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"><span style="font-family: Arial, Helvetica, sans-serif;"><b> (x<sup>2</sup>+y<sup>2</sup>) = 8xy
/ r<sup>2</sup> = 8xy/ (x<sup>2</sup>+y<sup>2</sup>) e (x<sup>2</sup>+y<sup>2</sup>)<sup>2</sup>
= 8xy<o:p></o:p></b></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"> finalmente r<sup>2</sup>= 4sen2</span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='mso-bidi-font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"> equivale a (x<sup>2</sup>+y<sup>2</sup>)<sup>2</sup>
= 8xy<o:p></o:p></span></b></span></div>
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<span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"><span style="font-family: Arial, Helvetica, sans-serif;"><b>2-
Transformar x<sup>2</sup>+y<sup>2</sup>=
4x em coordenadas polares.<o:p></o:p></b></span></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"> Subst x e y por x= r cos</span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='mso-bidi-font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">,</span><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"> y= r sen</span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='mso-bidi-font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> temos </span><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"> (r cos</span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='mso-bidi-font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">)<sup>2</sup>+(</span><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">r sen</span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='mso-bidi-font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">)<sup>2</sup>
= 4(r cos</span><!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:
normal'><span style='mso-bidi-font-size:12.0pt;line-height:115%;font-family:
"Cambria Math","serif"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">),
<o:p></o:p></span></b></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> onde
r<sup>2</sup>cos<sup>2</sup></span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='mso-bidi-font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">+r<sup>2</sup>sen<sup>2</sup></span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='mso-bidi-font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif"'><m:r>θ</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='mso-bidi-font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-fareast-font-family:
"Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>-</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 18.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image004.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">4r
cos</span><!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:
normal'><span style='mso-bidi-font-size:12.0pt;line-height:115%;font-family:
"Cambria Math","serif"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> = 0
simplifica ‘r’ e organiza <o:p></o:p></span></b></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> r (cos<sup>2</sup></span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='mso-bidi-font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">+sen<sup>2</sup></span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='mso-bidi-font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">)</span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='mso-bidi-font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-fareast-font-family:
"Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>-</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 9pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image005.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">4cos</span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='mso-bidi-font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> = 0
r.1</span><!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:
normal'><span style='mso-bidi-font-size:12.0pt;line-height:115%;font-family:
"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:
minor-fareast'><m:r>-</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 9pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image005.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">4
cos</span><!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:
normal'><span style='mso-bidi-font-size:12.0pt;line-height:115%;font-family:
"Cambria Math","serif"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">=
0, e <o:p></o:p></span></b></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> finalmente </span><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">x<sup>2</sup>+y<sup>2</sup>= 4x equivale a
</span><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">r
= 4 cos</span><!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:
normal'><span style='mso-bidi-font-size:12.0pt;line-height:115%;font-family:
"Cambria Math","serif"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"><o:p></o:p></span></b></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"><span style="font-family: Arial, Helvetica, sans-serif;"><b>3-
Ache a equação polar das equações dadas: <o:p></o:p></b></span></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"> a) x=2 polar
r cos</span><!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:
normal'><span style='mso-bidi-font-size:12.0pt;line-height:115%;font-family:
"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">=2<o:p></o:p></span></b></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"> b) y= -5 polar
r sen</span><!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:
normal'><span style='mso-bidi-font-size:12.0pt;line-height:115%;font-family:
"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;">= -5<o:p></o:p></span></b></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"> c) y= 2+x polar
r sen</span><!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:
normal'><span style='mso-bidi-font-size:12.0pt;line-height:115%;font-family:
"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"> = 2+r cos</span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='mso-bidi-font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 6.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image003.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> ... r (sen</span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='mso-bidi-font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>θ</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='mso-bidi-font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-fareast-font-family:
"Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>-</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 18.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image004.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">cos</span><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='mso-bidi-font-size:12.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman"'><m:r>
</m:r><m:r>θ</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="color: #0d0d0d; font-size: 12pt; line-height: 115%; position: relative; top: 5.5pt;"><v:shape id="_x0000_i1025" style="height: 16.5pt; width: 9.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\DOCUME~1\hercules\CONFIG~1\Temp\msohtmlclip1\01\clip_image006.png">
</v:imagedata></v:shape></span><!--[endif]--><span style="line-height: 115%; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">)
=2</span><span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"><o:p></o:p></span></b></span></div>
<div class="MsoNormal">
<span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"><span style="font-family: Arial, Helvetica, sans-serif;"><b> d) x<sup>2</sup>+y<sup>2</sup>= 4 polar
r = 2</b></span><o:p></o:p></span></div>
<br />
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="line-height: 115%; mso-bidi-font-size: 12.0pt;"><br /></span></div>
</div>
</div>
<div class="MsoNormal">
<div class="MsoNormal" style="margin-left: 35.45pt;">
<b><a href="http://calculo-hpf.blogspot.com.br/">VOLTAR</a></b></div>
</div>
</div>
hercules fontanahttp://www.blogger.com/profile/08624991926677457192noreply@blogger.com0tag:blogger.com,1999:blog-778878115735992586.post-78337214025044080522013-09-03T09:35:00.001-03:002013-11-07T18:28:38.177-02:00Integral-1<div class="separator" style="clear: both; text-align: center;">
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<div class="MsoNormal" style="margin-left: 2cm;">
<b><i><span style="font-family: inherit; font-size: large; line-height: 27px;">Conceitos<o:p></o:p></span></i></b></div>
<div class="MsoNormal" style="margin-left: 2cm;">
<b><i><span style="font-family: inherit; font-size: large; line-height: 27px;">Integral indefinida<o:p></o:p></span></i></b></div>
<div class="MsoNormal" style="margin-left: 2cm;">
<b><i><span style="font-family: inherit; font-size: large; line-height: 27px;">Integral definida<o:p></o:p></span></i></b></div>
<div class="MsoNormal" style="margin-left: 2cm;">
<b><i><span style="font-family: inherit; font-size: large; line-height: 27px;">Propriedades das integrais<o:p></o:p></span></i></b></div>
<div class="MsoListParagraphCxSpFirst" style="margin-left: 2cm;">
<b><i><span style="font-family: inherit; font-size: large; line-height: 27px;">Integral imprópria<o:p></o:p></span></i></b></div>
<div style="text-align: center;">
<span style="font-family: inherit; font-size: large;"><span style="line-height: 27px;"></span></span></div>
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<b><i><span style="font-family: inherit; font-size: large; line-height: 27px;">Integral imprópria com limites finitos</span></i></b><br />
<b><i><span style="font-family: inherit; font-size: large; line-height: 27px;">Integração pela aproximação: Regra Trapezoidal</span></i></b><br />
<b><i><span style="font-family: inherit; font-size: large; line-height: 27px;">Integração pela Regar parabólica de Simpson</span></i></b><br />
<b><i><span style="font-family: inherit; font-size: large; line-height: 27px;">Integração pela Fórmula prismoidal</span></i></b><br />
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<b><a href="http://calculo-hpf.blogspot.com/">VOLTAR</a></b></div>
hercules fontanahttp://www.blogger.com/profile/08624991926677457192noreply@blogger.com0tag:blogger.com,1999:blog-778878115735992586.post-92070266844593073662013-08-23T22:01:00.000-03:002013-10-12T21:36:41.785-03:00Limites<div class="separator" style="clear: both; text-align: center;">
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<div style="margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 106.35pt; margin-right: 0cm; margin-top: 0cm;">
<b><span style="font-family: inherit; font-size: large;"><br /></span></b>
<b><span style="font-family: inherit; font-size: large;">Conceitos<o:p></o:p></span></b></div>
<div style="margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 106.35pt; margin-right: 0cm; margin-top: 0cm;">
<b><span style="font-family: inherit; font-size: large;"><br /></span></b></div>
<div style="margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 106.35pt; margin-right: 0cm; margin-top: 0cm;">
<b><span style="font-family: inherit; font-size: large;">Cálculo dos limites <o:p></o:p></span></b></div>
<div style="margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 106.35pt; margin-right: 0cm; margin-top: 0cm;">
<b><span style="font-family: inherit; font-size: large;"> a) limites diretos e indiretos</span></b></div>
<div style="margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 106.35pt; margin-right: 0cm; margin-top: 0cm;">
<b><span style="font-family: inherit; font-size: large;"> b) limites fundamentais<o:p></o:p></span></b></div>
<div style="margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 106.35pt; margin-right: 0cm; margin-top: 0cm;">
<b><span style="font-family: inherit; font-size: large;"><br /></span></b></div>
<div style="margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 106.35pt; margin-right: 0cm; margin-top: 0cm;">
<b><span style="font-family: inherit; font-size: large;">Cálculo dos limites usando derivação<o:p></o:p></span></b></div>
<div style="margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 106.35pt; margin-right: 0cm; margin-top: 0cm;">
<b><span style="font-family: inherit; font-size: large;"> a) Regra de L'Hopitral<o:p></o:p></span></b></div>
<div style="margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 106.35pt; margin-right: 0cm; margin-top: 0cm;">
<b><span style="font-family: inherit; font-size: large;"> b) Cálculo de limites indeterminados<o:p></o:p></span></b></div>
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<b><a href="http://calculo-hpf.blogspot.com.br/">VOLTAR</a></b></div>
hercules fontanahttp://www.blogger.com/profile/08624991926677457192noreply@blogger.com0tag:blogger.com,1999:blog-778878115735992586.post-10592867803954331542013-08-23T00:44:00.000-03:002013-10-25T12:27:57.422-02:00Derivadas-1<div class="separator" style="clear: both; text-align: center;">
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<div class="MsoNormal" style="margin-left: 1.0cm;">
<b><span style="font-size: 14.0pt; line-height: 115%;">Derivadas I</span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> Derivadas de funções -
f(x)<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;">Derivadas II<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> Derivadas de funções em
cadeia - f(x)<sub>o</sub>g(x)<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> Derivadas de produto de
funções - f(x)g(x)<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> Derivadas de função
inversa - f<sup>-1</sup><o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> Derivadas de funções
hiperbólicas<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> Derivada de função
implícita – (ex: 3x=xy+2)<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> Derivadas de ordem
superior ou sucessivas f(x), f’(x), f<sup>n</sup>(x)<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> Derivação logarítmica<o:p></o:p></span></b></div>
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<b><span style="font-size: 14.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast;"> Derivadas parciais<o:p></o:p></span></b></div>
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<br />hercules fontanahttp://www.blogger.com/profile/08624991926677457192noreply@blogger.com0tag:blogger.com,1999:blog-778878115735992586.post-22440323191719728932013-08-10T21:33:00.003-03:002014-08-18T12:32:04.550-03:00Derivadas-2<div style="margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 2.0cm; margin-right: 0cm; margin-top: 0cm;">
<b><span style="font-size: 18pt;">Derivadas
de funções em cadeia - f(x)<sub>o</sub>g(x)</span></b><span style="font-size: 13.5pt;"><o:p></o:p></span></div>
<div style="margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 2.0cm; margin-right: 0cm; margin-top: 0cm;">
<b><span style="font-size: 18pt;">Derivadas
de produto de funções - f(x)g(x)</span></b><span style="font-size: 13.5pt;"><o:p></o:p></span></div>
<div style="margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 2.0cm; margin-right: 0cm; margin-top: 0cm;">
<b><span style="font-size: 18pt;">Derivadas
de função inversa - f<sup>-1</sup></span></b><span style="font-size: 13.5pt;"><o:p></o:p></span></div>
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<b><span style="font-size: 18pt;">Derivadas
de funções hiperbólicas</span></b><span style="font-size: 13.5pt;"><o:p></o:p></span></div>
<div style="margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 2.0cm; margin-right: 0cm; margin-top: 0cm;">
<b><span style="font-size: 18pt;">Derivada
de função implícita – (ex: 3x=xy+2)</span></b><span style="font-size: 13.5pt;"><o:p></o:p></span></div>
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<b><span style="font-size: 18pt;">Derivadas
sucessivas f(x), f’(x), f’’(x), f<sup>n</sup>(x)</span></b><span style="font-size: 13.5pt;"><o:p></o:p></span></div>
<div style="margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 2.0cm; margin-right: 0cm; margin-top: 0cm;">
<b><span style="font-size: 18pt;">Derivação
logarítmica</span></b><span style="font-size: 13.5pt;"><o:p></o:p></span></div>
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<b><span style="font-size: 18pt;">Derivadas
parciais</span></b><span style="font-size: 13.5pt;"><o:p></o:p></span></div>
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hercules fontanahttp://www.blogger.com/profile/08624991926677457192noreply@blogger.com0