<Text-field style="Heading 1" layout="Heading 1">Introdu\303\247\303\243o</Text-field>

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Cap\303\255tulo 14

Derivada de Fun\303\247\303\265es Impl\303\255citas

Muitas curvas interessantes n\303\243o podem ser escritas na forma expl\303\255cita 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mas podem ser dadas na forma impl\303\255cita

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

Sabemos que a inclina\303\247\303\243o da reta tangente a uma curva em um ponto \303\251 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 e, agora estamos confort\303\241veis em encontrar 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 para fun\303\247\303\265es expl\303\255citas. A diferencia\303\247\303\243o impl\303\255cita \303\251 uma t\303\251cnica que pode ser usada para encontrar LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtRiw2JVEjZHlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjtRJ25vcm1hbEYnLUYjNiQtRiw2JVEjZHhGJ0Y3RjpGPS8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGSS8lKWJldmVsbGVkR1EmZmFsc2VGJ0YrRj0= quando a fun\303\247\303\243o \303\251 dada implicitamente. \303\211 essencialmente a regra da cadeia aplicada \303\240 identidade 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

Como isto \303\251 realmente uma aplica\303\247\303\243o da derivada, este cap\303\255tulo consiste principalmente de exemplos. O primeiro exemplo examina um c\303\255rculo por ambas as formula\303\247\303\265es, da forma expl\303\255cita e da forma impl\303\255cita. O segundo exemplo examina uma fun\303\247\303\243o realmente impl\303\255cita, o Folium de Descartes. O \303\272ltimo exemplo estende a Regra da Pot\303\252ncia a todos os expoentes racionais.

O maplet TangentLinePlot (o Tutor Tangentes) pode ser usado para auxiliar com a visualiza\303\247\303\243o das retas tangentes ao gr\303\241fico de uma fun\303\247\303\243o impl\303\255cita definida.

<Text-field style="Heading 1" layout="Heading 1">\303\215ndice de Termos</Text-field>

Os seguintes termos, neste cap\303\255tulo, t\303\252m conex\303\243o com o Dicion\303\241rio do Maple; para mais informa\303\247\303\265es v\303\241 em Dicion\303\241rio Matem\303\241tico.

regra da cadeia

c\303\255rculo

conjugado complexo

n\303\272mero complexo

curva

derivada

diferenciada

diferencia\303\247\303\243o

expl\303\255cita

expoente

ponto flutuante

f\303\263lio(de Descartes)

fun\303\247\303\243o

gr\303\241fico

impl\303\255cita

inclina\303\247\303\243o

origem

par\303\242metro

polin\303\264mio

regra da pot\303\252ncia

prova

radius

fun\303\247\303\243o racional

real

taxa de varia\303\247\303\243o

raiz

satisfazer

conjunto

inclina\303\247\303\243o

solu\303\247\303\243o

resolver

sim\303\251trico

tangente

valor

vari\303\241vel

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Inicializa\303\247\303\243o</Text-field>

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUShyZXN0YXJ0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjhRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiO0YnRj0vJSZmZW5jZUdGPC8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0Y8LyUqc3ltbWV0cmljR0Y8LyUobGFyZ2VvcEdGPC8lLm1vdmFibGVsaW1pdHNHRjwvJSdhY2NlbnRHRjwvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJ0Y6Rj0=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

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Exemplo 14.1: <Hyperlink linktarget="Wks:../Dicion\303\241rio/T/tangent.mw" hyperlink="true" encoding="UTF-8">Retas Tangentes a um C\303\255rculo</Hyperlink></Text-field>

O c\303\255rculo centrado na origem e tendo raio 3 pode ser descrito como o conjunto de todos os pontos que satisfazem

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSNxMUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y4USdub3JtYWxGJ0YrRjpGPQ==

LywmKiQpSSJ4RzYiIiIjIiIiRikqJClJInlHRidGKEYpRikiIio=

Seja LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= um n\303\272mero 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 Porque ambos, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkmbXNxcnRHRiQ2Iy1GIzYnLUkjbW5HRiQ2JFEiOUYnRj4tRjs2LVEoJm1pbnVzO0YnRj5GQEZDRkVGR0ZJRktGTS9GUFEsMC4yMjIyMjIyZW1GJy9GU0Zbby1GIzYmRistSSVtc3VwR0YkNiUtRiw2JVEieEYnRjRGNy1GWjYkUSIyRidGPi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGK0Y+RitGPkYrRj5GK0Y+ e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYjNiYtRjs2LVEqJnVtaW51czA7RidGPkZARkNGRUZHRklGS0ZNL0ZQUSYwLjBlbUYnL0ZTRlotSSZtc3FydEdGJDYjLUYjNictSSNtbkdGJDYkUSI5RidGPi1GOzYtUSgmbWludXM7RidGPkZARkNGRUZHRklGS0ZNL0ZQUSwwLjIyMjIyMjJlbUYnL0ZTRmNvLUYjNiZGKy1JJW1zdXBHRiQ2JS1GLDYlUSJ4RidGNEY3LUZcbzYkUSIyRidGPi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGK0Y+RitGPkYrRj5GK0Y+RitGPg==, est\303\243o sobre o gr\303\241fico do c\303\255rculo, a equa\303\247\303\243o para o c\303\255rculo n\303\243o \303\251 uma fun\303\247\303\243o. (Lembre que ela define uma rela\303\247\303\243o.) Figura 14.1 fornece um gr\303\241fico para este c\303\255rculo,obtido no Maple via o comando implicitplot.

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

Figura 14.1 Gr\303\241fico do c\303\255rculo 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

A determina\303\247\303\243o da inclina\303\247\303\243o da reta tangente ao c\303\255rculo no 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 sobre o c\303\255rculo requer que encontremos 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 . A id\303\251ia por tr\303\241s da deriva\303\247\303\243o impl\303\255cita \303\251 pensar na equa\303\247\303\243o do c\303\255rculo como uma defini\303\247\303\243o impl\303\255cita de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= como uma fun\303\247\303\243o de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Isto significa que precisamos substituir todas as ocorr\303\252ncias de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= com LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGNEY3Rj5GPkY+RitGPg== tal que a equa\303\247\303\243o do c\303\255rculo fique:

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

LywmKiQpSSJ4RzYiIiIjIiIiRikqJCktSSJ5R0YnNiNGJkYoRilGKSIiKg==

Agora, ambos os lados desta identidade s\303\243o diferenciados em rela\303\247\303\243o a LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, levando a:

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSNxM0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y4USdub3JtYWxGJ0YrRjpGPQ==

LywmKiYiIiMiIiJJInhHNiJGJkYmKihGJUYmLUkieUdGKDYjRidGJi1JJWRpZmZHJSpwcm90ZWN0ZWRHNiRGKkYnRiZGJiIiIQ==

Note o uso da Regra da Cadeia para computar 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.

Agora \303\251 uma simples quest\303\243o de resolver uma outra derivada, cujo resultado \303\251:

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSNxNEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y4USdub3JtYWxGJ0YrRjpGPQ==

Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ5RzYiNiNJInhHRilGKywkKiZGKyIiIkYnISIiRi8=

Para colocar este resultado em uma forma consistente com a equa\303\247\303\243o original, substitua todas as ocorr\303\252ncias de 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 por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= de modo que a derivada seja dada por:

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

LyomSSNkeUc2IiIiIkkjZHhHRiUhIiIsJComSSJ4R0YlRiZJInlHRiVGKEYo

(14.1)

Por exemplo, a inclina\303\247\303\243o da reta tangente ao c\303\255rculo no ponto 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 \303\251:

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

LyomSSNkeUc2IiIiIkkjZHhHRiUhIiIsJComIyIiIyIiJkYmKUYtI0YmRixGJkYo

enquanto que, no 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, a inclina\303\247\303\243o da reta tangente ao c\303\255rculo \303\251:

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

LyomSSNkeUc2IiIiIkkjZHhHRiUhIiIsJComIyIiIyIiJkYmKUYtI0YmRixGJkYm

Que outros m\303\251todos poder\303\255amos usar para encontrar estas inclina\303\247\303\265es?

As partes superior e inferior do c\303\255rculo s\303\243o, separadamente, gr\303\241ficos das fun\303\247\303\265es expl\303\255citas:

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

LyZJInlHNiI2I0kkdG9wR0YlKiQpLCYiIioiIiIqJClJInhHRiUiIiNGLCEiIiNGLEYwRiw=

LyZJInlHNiI2I0kkYm90R0YlLCQqJCksJiIiKiIiIiokKUkieEdGJSIiI0YtISIiI0YtRjFGLUYy

As inclina\303\247\303\265es nos pontos da metade superior e da metade inferior podem ser encontradas derivando estas express\303\265es. Infelizmente, n\303\243o sabemos ainda como derivar a fun\303\247\303\243o raiz quadrada. (At\303\251 agora, a Regra de Pot\303\252ncia se aplica somente a expoentes inteiros.) Mas, deixando o Maple computar estas derivadas por n\303\263s, a inclina\303\247\303\243o da reta tangente em um ponto da metade superior do c\303\255rculo encontrada \303\251:

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

LyomSSNkeUc2IiIiIkkjZHhHRiUhIiIsJComKSwmIiIqRiYqJClJInhHRiUiIiNGJkYoI0YmRjFGKEYwRiZGKA==

A corre\303\247\303\243o deste resultado pode ser checada usando (14.1) e a equa\303\247\303\243o para a parte superior do c\303\255rculo:

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

LyomSSNkeUc2IiIiIkkjZHhHRiUhIiIsJComKSwmIiIqRiYqJClJInhHRiUiIiNGJkYoI0YmRjFGKEYwRiZGKA==

Do mesmo modo, a inclina\303\247\303\243o da reta tangente em um ponto da metade inferior do c\303\255rculo \303\251:

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

LyomSSNkeUc2IiIiIkkjZHhHRiUhIiIqJiksJiIiKkYmKiQpSSJ4R0YlIiIjRiZGKCNGJkYwRihGL0Ym

a qual concorda com:

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

LyomSSNkeUc2IiIiIkkjZHhHRiUhIiIqJiksJiIiKkYmKiQpSSJ4R0YlIiIjRiZGKCNGJkYwRihGL0Ym

que \303\251 o resultado de (14.1).

A express\303\243o para a derivada em (14.1) \303\251 definida somente se LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVElJm5lO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1JI21uR0YkNiRRIjBGJ0Y+Rj5GK0Y+. Isto faz sentido porque temos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4= quando LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiM0YnRj5GPkYrRj4= ou 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 e neste ponto as retas tangentes s\303\243o verticais. Estas caracter\303\255sticas, junto com as duas retas tangentes ao c\303\255rculo nos pontos onde LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMkYnRj5GPkYrRj4= , s\303\243o evidentes na Figura 14.2.

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Figura 14.2 O c\303\255rculo na Figura 14.1, junto com as duas retas tangentes em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjJGJ0Y5Rjk=

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Exemplo 14.2: Folium de Descartes</Text-field>

A forma geral para o Folium de Descartes \303\251 dada pela equa\303\247\303\243o impl\303\255cita:

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

LywmKiQpSSJ4RzYiIiIkIiIiRikqJClJInlHRidGKEYpRiksJCoqRihGKUkiYUdGJ0YpRiZGKUYsRilGKQ==

onde LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 um par\303\242metro.

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Visualizando o Folium de Descartes</Text-field>

Antes de analisar estas curvas ser\303\241 bom ter uma id\303\251ia da apar\303\252ncia destas curvas. A Figura 14.3 fornece uma amostra de anima\303\247\303\243o gr\303\241fica do Folium de Descartes para valores inteiros de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= deLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUYsNi1RKiZ1bWludXMwO0YnRi9GMkY1RjdGOUY7Rj1GPy9GQlEsMC4yMjIyMjIyZW1GJy9GRUZKLUkjbW5HRiQ2JFEiM0YnRi9GLw== a 3.

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Figura 14.3 Folium de Descartes para inteiros 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

Para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4=, o Folium se degenera na reta 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. Para todo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVElJm5lO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1JI21uR0YkNiRRIjBGJ0Y+LUY7Ni1RIixGJ0Y+RkBGQ0ZFRkdGSUZLRk1GT0ZSRj5GK0Y+ as curvas s\303\243o mais interessantes. Em particular, existem regi\303\265es onde existem tr\303\252s pontos sobre a curva para um \303\272nico valor de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= . (Isto \303\251 de se esperar porque toda equa\303\247\303\243o c\303\272bica com coeficientes com valores reais tem tr\303\252s ra\303\255zes reais ou ra\303\255zes complexas --- e ra\303\255zes complexas aparecem em pares conjugados.)

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Encontrando a Inclina\303\247\303\243o por Deriva\303\247\303\243o Impl\303\255cita </Text-field>

Deriva\303\247\303\243o impl\303\255cita ser\303\241 usada para encontrar a inclina\303\247\303\243o da reta tangente em cada ponto sobre o Folium de Descartes. Para este fim, substitua cada letra LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= por 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 para obter:

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSNyMkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y4USdub3JtYWxGJ0YrRjpGPQ==

LywmKiQpSSJ4RzYiIiIkIiIiRikqJCktSSJ5R0YnNiNGJkYoRilGKSwkKipGKEYpSSJhR0YnRilGJkYpRixGKUYp

E, ent\303\243o, use a regra da cadeia para derivar em rela\303\247\303\243o a LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= ambos os lados desta identidade, obtendo:

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSNyM0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y4USdub3JtYWxGJ0YrRjpGPQ==

LywmKiYiIiQiIiIpSSJ4RzYiIiIjRiZGJiooRiVGJiktSSJ5R0YpNiNGKEYqRiYtSSVkaWZmRyUqcHJvdGVjdGVkRzYkRi1GKEYmRiYsJiooRiVGJkkiYUdGKUYmRi1GJkYmKipGJUYmRjZGJkYoRiZGMEYmRiY=

Resolvendo para a nova derivada d\303\241:

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSNyNEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y4USdub3JtYWxGJ0YrRjpGPQ==

Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ5RzYiNiNJInhHRilGKyomLCYqJClGKyIiIyIiIiEiIiomSSJhR0YpRjFGJ0YxRjFGMSwmKiQpRidGMEYxRjEqJkY0RjFGK0YxRjJGMg==

Substituindo 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 pelo simples LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, coloca a derivada na forma:

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

LyomSSNkeUc2IiIiIkkjZHhHRiUhIiIqJiwmKiQpSSJ4R0YlIiIjRiZGKComSSJhR0YlRiZJInlHRiVGJkYmRiYsJiokKUYxRi5GJkYmKiZGMEYmRi1GJkYoRig=

N\303\243o nos surpreende que uma ferramenta t\303\243o poderosa como o Maple tenha um comando embutido para calcular derivadas impl\303\255citas. Seu uso aqui leva \303\240 seguinte derivada:

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

KiYsJiokKUkieEc2IiIiIyIiIiEiIiomSSJhR0YnRilJInlHRidGKUYpRiksJiokKUYtRihGKUYpKiZGLEYpRiZGKUYqRio=

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Pontos sobre a Curva com Tangentes Horizontais </Text-field>

Esta informa\303\247\303\243o pode ser usada para identificar alguns pontos especiais sobre estas curvas. Por exemplo, a reta tangente \303\240 curva \303\251 horizontal nos pontos sobre a curva onde a inclina\303\247\303\243o \303\251 zero, isto \303\251, nos pontosLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2J0YrLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y6LyUpc3RyZXRjaHlHRjovJSpzeW1tZXRyaWNHRjovJShsYXJnZW9wR0Y6LyUubW92YWJsZWxpbWl0c0dGOi8lJ2FjY2VudEdGOi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkktRiM2Ji1GMjYtUSIoRidGNS9GOVEldHJ1ZUYnRjsvRj5GUkY/RkFGQ0ZFL0ZIUSwwLjE2NjY2NjdlbUYnL0ZLRlUtRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHRlIvRjZRJ2l0YWxpY0YnLUYyNi1RIixGJ0Y1RjgvRjxGUkY9Rj9GQUZDRkVGRy9GS1EsMC4zMzMzMzMzZW1GJy1GLDYlUSJ5RidGZm5GaG5GNS1GMjYtUSIpRidGNUZRRjtGU0Y/RkFGQ0ZFRlQvRktRLDAuMTExMTExMWVtRidGNUYrRjVGK0Y1 que satisfazem ambas as seguintes equa\303\247\303\265es.

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

LywmKiQpSSJ4RzYiIiIkIiIiRikqJClJInlHRidGKEYpRiksJCoqRihGKUkiYUdGJ0YpRiZGKUYsRilGKQ==

LywmKiQpSSJ4RzYiIiIjIiIiRikqJkkiYUdGJ0YpSSJ5R0YnRikhIiIiIiE=

Maple informa as solu\303\247\303\265es deste par de equa\303\247\303\265es como:

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

NyQ8JC9JInhHNiIiIiEvSSJ5R0YmRic8JC9GJSomLUknUm9vdE9mRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiMsJiokKUkjX1pHRi8iIiQiIiJGOCIiIyEiIkY4SSJhR0YmRjgvRikqJilGLUY5RjhGO0Y4

A nota\303\247\303\243o RootOf \303\251 o modo de o Maple listar concisamente todas as ra\303\255zes reais e complexas de um polin\303\264mio. Podemos for\303\247ar a expans\303\243o total das solu\303\247\303\265es com o comando allvalues . O resultado \303\251:

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

NyY8JC9JInhHNiIiIiEvSSJ5R0YmRic8JC9GJSomKSIiIyMiIiIiIiRGMEkiYUdGJkYwL0YpKiYpRi4jRi5GMUYwRjJGMDwkL0YlKiYsJiomI0YwRi5GMEYtRjAhIiIqKComRjxGMF4jRjBGMEYwKUYxRjxGMEYtRjBGMEYwRjJGMC9GKSomKUY6Ri5GMEYyRjA8JC9GJSomLCZGO0Y9KigsJEY/RjBGMEZBRjBGLUYwRj1GMEYyRjAvRikqJilGSEYuRjBGMkYw

Somente as solu\303\247\303\265es reais s\303\243o de interesse para n\303\263s; por isso removemos todas as solu\303\247\303\265es que tenham partes imagin\303\241rias, usando o comando remove:

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

NyQ8JC9JInhHNiIiIiEvSSJ5R0YmRic8JC9GJSomKSIiIyMiIiIiIiRGMEkiYUdGJkYwL0YpKiYpRi4jRi5GMUYwRjJGMA==

Isto leva, para cada valor de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVElJm5lO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1JI21uR0YkNiRRIjBGJ0Y+Rj5GK0Y+, a dois pontos com tangentes horizontais, a saber, os pontos:

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

NiQ3JCIiIUYkNyQqJikiIiMjIiIiIiIkRipJImFHNiJGKiomKUYoI0YoRitGKkYsRio=

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Pontos Sobre a Curva com Tangentes Verticais </Text-field>

Pelo mesmo motivo, a inclina\303\247\303\243o da reta tangente \303\240 curva \303\251 indefinida nos pontos que satisfazem a duas condi\303\247\303\265es:

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSRyMTBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GOFEnbm9ybWFsRidGK0Y6Rj0=

LywmKiQpSSJ4RzYiIiIkIiIiRikqJClJInlHRidGKEYpRiksJCoqRihGKUkiYUdGJ0YpRiZGKUYsRilGKQ==

LywmKiQpSSJ5RzYiIiIjIiIiISIiKiZJImFHRidGKUkieEdGJ0YpRikiIiE=

As solu\303\247\303\265es reais encontradas, deste sistema, s\303\243o:

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

NiQ3JCIiIUYkNyQqJikiIiMjRigiIiQiIiJJImFHNiJGKyomKUYoI0YrRipGK0YsRis=

Note que a origem tem ambas as retas tangentes, uma horizontal e uma vertical, e que os outros pontos s\303\243o sim\303\251tricos em rela\303\247\303\243o \303\240 reta LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRInhGJ0Y0RjdGPkYrRj4=. (Um exame mais minuncioso na equa\303\247\303\243o original e na f\303\263mula para a inclina\303\247\303\243o explica porque esta - e outras simetrias - s\303\243o esperadas.)

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Pontos Sobre a Curva com <Equation executable="false" style="2D Math_16" input-equation="" display="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">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</Equation> </Text-field>

Pontos onde a inclina\303\247\303\243o da reta tangente \303\251 1 s\303\243o solu\303\247\303\265es para as equa\303\247\303\265es:

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSRyMTRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GOFEnbm9ybWFsRidGK0Y6Rj0=

LywmKiQpSSJ4RzYiIiIkIiIiRikqJClJInlHRidGKEYpRiksJCoqRihGKUkiYUdGJ0YpRiZGKUYsRilGKQ==

LyomLCYqJClJInhHNiIiIiMiIiIhIiIqJkkiYUdGKEYqSSJ5R0YoRipGKkYqLCYqJClGLkYpRipGKiomRi1GKkYnRipGK0YrRio=

As solu\303\247\303\265es reais encontradas para este sistema s\303\243o:

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

NiQ3JCoqLCYqJiMiIiIiIiNGKCkiIiRGJ0YoRigqJkYnRigpLCZGKyEiIiomRilGKEYqRihGKEYnRihGL0YoSSJhRzYiRigsKiokKUYlRilGKEYoRihGKEYmRi9GLEYoRigsKiokRipGKEYoKiRGLUYoRi9GKEYvRjRGKEYvKiZGJUYoRjFGKDckKiosJkYmRihGLEYoRihGMUYoLCoqJClGPEYpRihGKEYoRihGJkYvRixGL0YoLCpGN0YoRjhGKEYoRi9GPkYoRi8qJkY8RihGMUYo

ou com aproxima\303\247\303\265es de ponto flutuante para raizes quadradas:

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

NiQ3JCwkKiYkIitCL2wxNyEiKiIiIkkiYUc2IkYpRiksJComJCIrV1ErYV8hIzVGKUYqRilGKTckLCQqJiQiK11RK2FfRjBGKUYqRilGKSwkKiYkIitDL2wxN0YoRilGKkYpRik=

Novamente, note a simetria nestas solu\303\247\303\265es. Note tamb\303\251m que estas solu\303\247\303\265es n\303\243o s\303\243o corretas para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4=. O fato de que n\303\243o existem pontos sobre o gr\303\241fico com inclina\303\247\303\243o 1 quando LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4= pode ser visto da janela na anima\303\247\303\243o com LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj5GPkYrRj4= assim como da resposta do Maple para o seguinte comando:

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

NyI=

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Coment\303\241rios de Conclus\303\243o: Forma Expl\303\255cita para Folium de Descartes </Text-field>

No in\303\255cio deste exemplo, dizemos que n\303\243o era poss\303\255vel encontrar uma representa\303\247\303\243o expl\303\255cita para oFolium de Descartes. Embora seja tamb\303\251m verdade que cada Folium n\303\243o \303\251 o gr\303\241fico de uma fun\303\247\303\243o, \303\251 poss\303\255vel encontrar uma f\303\263rmula expl\303\255cita para cada segmento da curva.

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

L0kieUc2IiwmKiYjIiIiIiIjRigpLCYqJiIiJUYoKUkieEdGJCIiJEYoISIiKiZGLUYoKSwmKihGLUYoRi5GKClJImFHRiRGMEYoRjEqJClGLyIiJ0YoRihGJ0YoRigjRihGMEYoRigqKkYpRihGN0YoRi9GKEYqRjFGKA==

L0kieUc2IiwoKiYjIiIiIiIlRigpLCYqJkYpRigpSSJ4R0YkIiIkRighIiIqJkYpRigpLCYqKEYpRihGLUYoKUkiYUdGJEYvRihGMCokKUYuIiInRihGKCNGKCIiI0YoRigjRihGL0YoRjAqKEY2RihGLkYoRipGMEYwKigqJkY6RiheI0YoRihGKClGL0Y6RigsJiomRjpGKEYqRihGKCoqRjtGKEY2RihGLkYoRipGMEYwRihGKA==

L0kieUc2IiwoKiYjIiIiIiIlRigpLCYqJkYpRigpSSJ4R0YkIiIkRighIiIqJkYpRigpLCYqKEYpRihGLUYoKUkiYUdGJEYvRihGMCokKUYuIiInRihGKCNGKCIiI0YoRigjRihGL0YoRjAqKEY2RihGLkYoRipGMEYwKigsJComRjpGKF4jRihGKEYoRigpRi9GOkYoLCYqJkY6RihGKkYoRigqKkY7RihGNkYoRi5GKEYqRjBGMEYoRjA=

A primeira das tr\303\252s solu\303\247\303\265es \303\251 sempre real. As outras duas ou s\303\243o reais ou complexos conjugados; quando elas s\303\243o reais o Folium tem tr\303\252s pontos para um \303\272nico valor de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Quando elas s\303\243o complexos conjugados existe somente um ponto sobre a curva para cada valor de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=; e na transi\303\247\303\243o entre estes estados -- o \303\272nico valor de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= com dois pontos sobre a curva -- estas duas solu\303\247\303\265es se reduzem a uma \303\272nica solu\303\247\303\243o repetida.

Mesmo se pud\303\251ssemos decidir qual dessas tr\303\252s f\303\263rmulas usar, as derivadas seriam muito complicadas. Por compara\303\247\303\243o, a computa\303\247\303\243o da derivada pela deriva\303\247\303\243o impl\303\255cita foi quase sem esfor\303\247o.

<Text-field style="Heading 1" readonly="true" layout="Heading 1">Maple T.A. Maple-Graded Question</Text-field>

<Text-field style="Heading 2" layout="Heading 2">Algorithmic Variables</Text-field>

In the following execution group, add an algorithmic variable.

with(RandomTools): randomize(): nnn1 := Generate(integer(range=1..6)): nn1 := Generate(choose([-nnn1,nnn1])): nnn2 := Generate(integer(range=1..6)): nn2 := Generate(choose([-nnn2,nnn2])): nnn3 := Generate(integer(range=1..6)): nn3 := Generate(choose([-nnn3,nnn3])): nn4 := Generate(integer(range=1..4)): nn5 := Generate(integer(range=1..4)): nn6 := Generate(integer(range=1..4)): nn7 := Generate(integer(range=1..4)): fn := nn1 * x^nn4 + nn2 * x^nn5 * y^nn6 + nn3 * y^nn7 = 0; sn := implicitdiff(fn,y,x);

LywoKiRJInhHNiIiIiQiIiUqJkYlRidJInlHRiYiIiIhIiYqJEYqRichIiIiIiE=

LCQqKEkieEc2IiIiIywmISIlIiIiSSJ5R0YlIiImRiksJiokRiQiIiRGKyokRipGJkYuISIiISIk

JSFH

<Text-field style="Heading 1" layout="Heading 1">Quest\303\243o 14.1</Text-field>

In the following text region, enter the full contents of the question.

Encontre LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JkYrLUkmbWZyYWNHRiQ2KC1GIzYkLUYsNiVRI2R5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0Y9USdub3JtYWxGJy1GIzYkLUYsNiVRI2R4RidGOUY8Rj8vJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRksvJSliZXZlbGxlZEdRJmZhbHNlRidGK0Y/RitGPw== para

`$fn`

JSFH

<Text-field style="Heading 2" layout="Heading 2">Answer</Text-field>

Enter Maple code in 1-D Math that evaluates to the correct answer. Add additional execution groups as needed.

JSFHsn;

<Text-field style="Heading 2" layout="Heading 2">Evaluate Student's Response</Text-field>

Enter Maple code to evaluate a student's response. To add additional Maple functionality, use the Answer input region.

evalb(simplify(`$ANSWER`-`$RESPONSE`)=0);

<Text-field style="Heading 2" layout="Heading 2">Hints</Text-field>

Enter your hints in the following table.

Before beginning, think of y as y(x)

Differentiate with respect to x, and then solve for 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

Don't forget to use the product rule if you see 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

with(StringTools): with(DocumentTools): response := GetProperty(`TextArea2`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Before beginning, think of </mtext><mtext>y</mtext><mtext> as </mtext><mtext>y(x)</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

with(StringTools): with(DocumentTools): response := GetProperty(`TextArea2`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Differentiate with respect to </mtext><mtext>x</mtext><mtext>, and then solve for </mtext><mstyle fontfamily='serif' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi>dy</mi><mi>dx</mi></mfrac></mrow></mstyle><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

with(StringTools): with(DocumentTools): response := GetProperty(`TextArea2`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext></mtext><mtext> </mtext><mtext>Don't forget to use the product rule if you see </mtext><mstyle fontfamily='serif' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>x</mi><mo fontfamily='serif' lspace='0.0em' rspace='0.0em'>⋅</mo><mi>y</mi></mrow></mstyle><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

<Text-field style="Heading 2" layout="Heading 2">Feedback</Text-field>

In the following text region, enter feedback to an incorrect response.

with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea2`, `value`); ANSWER := sn; if evalb(simplify(ANSWER-eval(parse(StudentResponse)))=0) then feedback:=cat("<math><mrow><mtext mathvariant='bold'>Correct!&NewLine;</mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext></mrow></math>"); else if StudentResponse = "" then StudentResponse:="<NO RESPONSE>"; fi; feedback:=cat("<math><mrow><mtext mathvariant='bold'>Your answer is incorrect. </mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, "<mtext mathvariant='bold'>Correct Answer: </mtext><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mfrac><mrow><mn>3</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mfenced open='(' close=')' separators=','><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>4</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>5</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>y</mi></mrow></mrow></mfenced></mrow><mrow><mrow><mrow><mn>5</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>3</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>3</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>y</mi><mn>2</mn></msup></mrow></mrow></mrow></mfrac></mrow></mrow></mstyle></math><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext></mtext><mtext> </mtext><mtext></mtext><mtext>&NewLine;</mtext></mrow>", "`$RESPONSE`", StudentResponse)); feedback:=SubstituteAll(feedback, "`$ANSWER`", "<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mfrac><mrow><mn>3</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>2</mn></msup><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mfenced open='(' close=')' separators=','><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mn>4</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>5</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>y</mi></mrow></mrow></mfenced></mrow><mrow><mrow><mrow><mn>5</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>3</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>3</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>y</mi><mn>2</mn></msup></mrow></mrow></mrow></mfrac></mrow></mrow></mstyle></math>"); feedback:=cat(feedback, "</mrow></math>"); fi; with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Feedback", [[MathMLViewer('value' = feedback, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): if feedback <> "" then Maplets[Display](maplet); fi;

<Text-field style="Heading 1" readonly="true" layout="Heading 1">Maple T.A. Maple-Graded Question</Text-field>

Using the Maple-graded question type, you create a question that uses Maple functionality when creating the correct answer and determining if the student's response is correct. The Maple-graded question type has an option to plot the student's response. To include the plot option, insert the corresponding task template. For information on creating questions, making assignments, and exporting Maple T.A. course modules, see Overview of Maple T.A. Integration.

<Text-field style="Heading 2" layout="Heading 2">Algorithmic Variables</Text-field>

Algorithmic variables can be used to create a question that contains randomly generated parameters. You can refer to algorithmic variables in the Question, Answer, Hints, and Feedback input regions, as well as in other variable definitions. To reference an algorithmic variable, include "`$variable`" as text or 2-D Math, for example, x := `$myvariable`. Adding algorithmic variables to the question is optional. In the following execution group, add an algorithmic variable. To include more variables, add more execution groups. If your assignment contains more than one algorithmic variable, ensure the variable names are unique.

with(RandomTools): randomize(): a1 := Generate(integer(range=-5..5)): a2 := Generate(integer(range=-5..5)): a3 := Generate(integer(range=-5..5)): m1 := Generate(integer(range=-2..2)): while (m1=0) do m1 := Generate(integer(range=-2..2)) end do: m2 := Generate(integer(range=-2..2)): n1 := Generate(integer(range=-2..2)): n2 := Generate(integer(range=-2..2)): while (n2=0) do n2 := Generate(integer(range=-2..2)) end do: r1 := Generate(choose([-10..-1,1..10])): c1 := Generate(integer(range=r1)): p1 := Generate(choose([sin,cos,tan])): fn1 := a1*x^m1+a2*y^n1+p1(a3*x^m2*y^n2)=c1: fn2 := a1*x^m1*y^n1+p1(a2*x^m2+a3*y^n2)=c1: fn3 := Generate(choose([fn1,fn2])); ans2 := implicitdiff(fn3,y,x);

LywmKiZJInhHNiIiIiNJInlHRiYhIiJGJy1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYjLCQqJEYlRikiIiYiIiIiIig=

LCQqKEkieUc2IiIiIiwmKiRJInhHRiUiIiQiIiUqJi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLCQqJEYpISIiIiImRiZGJEYmRjZGJkYpISIlI0YmIiIj

JSFH

<Text-field style="Heading 1" layout="Heading 1">Quest\303\243o 14.2</Text-field>

The question can contain text, 2-D Math, plots, images, and algorithmic variables. To insert a plot in the question, use the Plot Component. In the following text region, enter the full contents of the question.

JSFH

<Text-field style="Heading 2" layout="Heading 2">Answer</Text-field>

To evaluate a student's response, enter the correct answer. Complete each line of code with a semicolon. The last line must evaluate to an expression that will be stored as the variable `$ANSWER`. Enter Maple code in 1-D Math that evaluates to the correct answer. Add additional execution groups as needed.

JSFHans2;

<Text-field style="Heading 2" layout="Heading 2">Evaluate Student's Response</Text-field>

To evaluate a student's response, you must evalute to a Boolean value (true or false). The variable `$RESPONSE` is automatically initialized to the student's response. Using `$ANSWER` (the correct answer) and `$RESPONSE` (the student response), one example of evaluating to a Boolean value is, evalb(`$ANSWER`-`$RESPONSE`=0); Enter Maple code to evaluate a student's response. To add additional Maple functionality, use the Answer input region.

evalb(simplify(`$ANSWER`-`$RESPONSE`)=0);

<Text-field style="Heading 2" layout="Heading 2">Hints</Text-field>

A question can offer hints to students when requested. Hints can contain text, 2-D Math, and algorithmic variables. Adding hints to the question is optional. Enter your hints in the following table. You can provide up to three hints.

Before beginning, think of y as y(x)

Differentiate with respect to x, and then solve for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYsNiVRI2R5RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GLDYlUSNkeEYnRjVGOC8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGQy8lKWJldmVsbGVkR0Y3RitGOA==

Don't forget to use the Chain Rule, if necessary.

with(StringTools): with(DocumentTools): response := GetProperty(`TextArea3`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Differentiate with respect to </mtext><mtext>x</mtext><mtext>, and then solve for </mtext><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac background='#000000'><mi mathbackground='#000000' mathvariant='normal'>dy</mi><mi mathbackground='#000000' mathvariant='normal'>dx</mi></mfrac></mrow></mstyle><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

with(StringTools): with(DocumentTools): response := GetProperty(`TextArea3`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Don't forget to use the Chain Rule, if necessary.</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

<Text-field style="Heading 2" layout="Heading 2">Feedback</Text-field>

A question can display feedback when a student provides an incorrect response. The feedback can contain text, 2-D Math, and algorithmic variables. The feedback can also refer to `$RESPONSE` (the student response) and `$ANSWER` (the correct answer). Adding feedback to the question is optional. In the following text region, enter feedback to an incorrect response.

Replace this text with feedback.

with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea3`, `value`); ANSWER := ans2; if evalb(simplify(ANSWER-eval(parse(StudentResponse)))=0) then feedback:=cat("<math><mrow><mtext mathvariant='bold'>Correct!&NewLine;</mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext></mrow></math>"); else if StudentResponse = "" then StudentResponse:="<NO RESPONSE>"; fi; feedback:=cat("<math><mrow><mtext mathvariant='bold'>Your answer is incorrect. </mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, "<mtext mathvariant='bold'>Correct Answer: </mtext><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mfrac><mrow><mi>y</mi><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mfenced open='(' close=')' separators=','><mrow><mrow><mn>4</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>3</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>5</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mrow><mi mathvariant='normal'>sin</mi><mo lspace='0.0em' rspace='0.0em'>⁡</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mn>5</mn></mrow><mrow><mi>x</mi></mrow></mfrac></mrow></mfenced></mrow><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>y</mi></mrow></mrow></mfenced></mrow><mrow><msup><mi>x</mi><mn>4</mn></msup></mrow></mfrac></mrow></mrow></mstyle></math><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext>&NewLine;</mtext></mrow>", "`$RESPONSE`", StudentResponse)); feedback:=SubstituteAll(feedback, "`$ANSWER`", "<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mfrac><mrow><mi>y</mi><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mfenced open='(' close=')' separators=','><mrow><mrow><mn>4</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msup><mi>x</mi><mn>3</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>5</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mrow><mi mathvariant='normal'>sin</mi><mo lspace='0.0em' rspace='0.0em'>⁡</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mn>5</mn></mrow><mrow><mi>x</mi></mrow></mfrac></mrow></mfenced></mrow><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>y</mi></mrow></mrow></mfenced></mrow><mrow><msup><mi>x</mi><mn>4</mn></msup></mrow></mfrac></mrow></mrow></mstyle></math>"); feedback:=cat(feedback, "</mrow></math>"); fi; with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Feedback", [[MathMLViewer('value' = feedback, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): if feedback <> "" then Maplets[Display](maplet); fi;

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Exemplo 14.3: A Regra de Pot\303\252ncia para Expoentes Racionais</Text-field>

No Exemplo 14.1 (trabalhando sem Maple), fomos incapazes de encontrar a inclina\303\247\303\243o da reta tangente em um ponto sobre a parte superior ou inferior de um c\303\255rculo, porque n\303\243o sab\303\255amos como derivar a fun\303\247\303\243o raiz quadrada. No entanto poder\303\255amos ter derivado este resultado para a fun\303\247\303\243o raiz quadrada usando a defini\303\247\303\243o de derivada; \303\251 muito mais eficiente e \303\272til manusear todos os expoentes racionais simultaneamente. Neste exemplo a deriva\303\247\303\243o impl\303\255cita ser\303\241 usada para mostrar que a Regra de Pot\303\252ncia se aplica para todos os expoentes racionais. Mostraremos que, se 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 com LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEicUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= inteiros e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJxRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVElJm5lO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1JI21uR0YkNiRRIjBGJ0Y+Rj5GK0Y+, ent\303\243o:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtRiw2JVEiZEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GO1Enbm9ybWFsRictRiM2JC1GLDYlUSNkeEYnRjdGOkY9LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZJLyUpYmV2ZWxsZWRHUSZmYWxzZUYnRitGPQ== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3VwR0YkNiUtRiw2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYlUSJuRidGNUY4LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrL0Y5USdub3JtYWxGJw== = 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

A chave para converter a forma expl\303\255cita:

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSNzMUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y4USdub3JtYWxGJ0YrRjpGPQ==

L0kieUc2IilJInhHRiRJIm5HRiQ=

em representa\303\247\303\243o impl\303\255cita com expoentes inteiros:

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSNzMkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y4USdub3JtYWxGJ0YrRjpGPQ==

LylJInlHNiJJInFHRiUpSSJ4R0YlSSJwR0Yl

Para preparar para a deriva\303\247\303\243o impl\303\255cita, lembremo-nos (e ao Maple) de que 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. A equa\303\247\303\243o definida \303\251, portanto:

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSNzM0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y4USdub3JtYWxGJ0YrRjpGPQ==

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A deriva\303\247\303\243o de ambos os lados da equa\303\247\303\243o em rela\303\247\303\243o a LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= d\303\241:

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSNzNEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y4USdub3JtYWxGJ0YrRjpGPQ==

LyoqKS1JInlHNiI2I0kieEdGJ0kicUdGJyIiIkYqRistSSVkaWZmRyUqcHJvdGVjdGVkRzYkRiVGKUYrRiUhIiIqKClGKUkicEdGJ0YrRjNGK0YpRjA=

Resolvendo para a outra derivada temos:

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

LyomSSNkeUc2IiIiIkkjZHhHRiUhIiIqKilJInhHRiUsJkkicEdGJUYmRiZGKEYmRi1GJilJInlHRiUsJkkicUdGJUYoRiZGJkYmRjFGKA==

Gostar\303\255amos de expressar esta derivada em termos de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. A rela\303\247\303\243o expl\303\255cita LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUklbXN1cEdGJDYlLUYsNiVRInhGJ0Y0RjctRiw2JVEibkYnRjRGNy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGK0Y+RitGPg== com 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 (logo 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 ) permite que a derivada seja reescrita como:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtRiw2JVEjcXNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSM6PUYnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZTLUYjNixGKy1GIzYnLUYsNiVRKXNpbXBsaWZ5RidGNkY5LUY9Ni1RMCZBcHBseUZ1bmN0aW9uO0YnRkBGQkZFRkdGSUZLRk1GTy9GUlEmMC4wZW1GJy9GVUZbby1JKG1mZW5jZWRHRiQ2JC1GIzYnRistRiM2Jy1GLDYlUSVldmFsRidGNkY5RmduLUZebzYkLUYjNictRiw2JVEjczZGJ0Y2RjktRj02LVEiLEYnRkBGQi9GRkY4RkdGSUZLRk1GT0Zqbi9GVVEsMC4zMzMzMzMzZW1GJy1GXm82Ji1GIzYoLUYsNiVRI3MxRidGNkY5Rl5wLUYjNigtRiw2JVEicEYnRjZGOS1GPTYtUSI9RidGQEZCRkVGR0ZJRktGTUZPRlFGVC1GIzYmLUYsNiVRIm5GJ0Y2RjktRj02LVExJkludmlzaWJsZVRpbWVzO0YnRkBGQkZFRkdGSUZLRk1GT0ZqbkZcby1GLDYlUSJxRidGNkY5RkBGKy8lK2V4ZWN1dGFibGVHRkRGQEYrRl5yRkBGQC8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZeckZARkBGXnJGQEYrRl5yRkBGQEZeckZARistSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuNWVtRicvJSZkZXB0aEdGW3MvJSpsaW5lYnJlYWtHUSVhdXRvRictRj02LVEpYXNzdW1pbmdGJ0ZARkJGRUZHRklGS0ZNRk9Gam5GXG9GZnItRiM2J0Zbci1GPTYtUSM6OkYnRkBGQkZFRkdGSUZLRk1GT0ZqbkZcby1GLDYlUShpbnRlZ2VyRidGNkY5Rl5yRkBGK0ZeckZARitGXnJGQEYrRl5yRkAtRj02LVEiOkYnRkBGQkZFRkdGSUZLRk1GT0ZRRlRGXnJGQA==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSNxc0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y4USdub3JtYWxGJ0YrRjpGPQ==

LyomSSNkeUc2IiIiIkkjZHhHRiUhIiIqJilJInhHRiUsJkYmRihJIm5HRiVGJkYmRi1GJg==

Isto conclui a prova de que a Regra de Pot\303\252ncia se aplica para todos os expoentes racionais.

<Text-field style="Heading 1" readonly="true" layout="Heading 1">Maple T.A. Maple-Graded Question</Text-field>

<Text-field style="Heading 2" layout="Heading 2">Algorithmic Variables</Text-field>

with(RandomTools): randomize(): a4 := Generate(integer(range=-5..5)): a5 := Generate(integer(range=-5..5)): a6 := Generate(integer(range=-5..5)): m3 := Generate(choose([1,2,3])): m4 := Generate(choose([1,2,3])): n3 := Generate(choose([2,3])): while (m3=n3) do n3 := Generate(choose([2,3])) end do: n4 := Generate(choose([2,3])): while (m4=n4) do n4 := Generate(choose([2,3])) end do: r2 := Generate(choose([-10..-1,1..10])): c2 := Generate(integer(range=r2)): fn4 := (a4*x+a5*y)^(m3/n3)+a6*x^m4*y^n4=c2: fn5 := a4*x^m3+y^n3+(a5*x^m4+a6*y^n4)^(m4/n4)=c2: fn6 := Generate(choose([fn4,fn5])); ans3 := implicitdiff(fn6,y,x);

LywoKiRJInhHNiIiIiNGJyokSSJ5R0YmIiIkIiIiKiYiIiYjRitGJyokRiVGKiNGKkYnRi1GJw==

LCQqKEkieEc2IiIiIiwmIiIpRiYqKCIiJiNGJiIiIyokRiQiIiRGK0YkRiYiI1hGJkkieUdGJSEiIyMhIiIiIic=

JSFH

<Text-field style="Heading 1" layout="Heading 1">Quest\303\243o 14.3</Text-field>

JSFH

<Text-field style="Heading 2" layout="Heading 2">Answer</Text-field>

JSFHans3;

<Text-field style="Heading 2" layout="Heading 2">Evaluate Student's Response</Text-field>

evalb(simplify(`$ANSWER`-`$RESPONSE`)=0);

<Text-field style="Heading 2" layout="Heading 2">Hints</Text-field>

Before beginning, think of y as y(x)

Don't forget to use the Chain Rule, if necessary.

with(StringTools): with(DocumentTools): response := GetProperty(`TextArea1`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Differentiate with respect to </mtext><mtext>x</mtext><mtext>, and then solve for </mtext><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac background='#000000'><mi mathbackground='#000000' mathvariant='normal'>dy</mi><mi mathbackground='#000000' mathvariant='normal'>dx</mi></mfrac></mrow></mstyle><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

with(StringTools): with(DocumentTools): response := GetProperty(`TextArea1`, `value`); if response = `` then response := "</mtext><mtext><NO RESPONSE></mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Don't forget to use the Chain Rule, if necessary.</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

<Text-field style="Heading 2" layout="Heading 2">Feedback</Text-field>

Replace this text with feedback.

with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea1`, `value`); ANSWER := ans3; if evalb(simplify(ANSWER-eval(parse(StudentResponse)))=0) then feedback:=cat("<math><mrow><mtext mathvariant='bold'>Correct!&NewLine;</mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext></mrow></math>"); else if StudentResponse = "" then StudentResponse:="<NO RESPONSE>"; fi; feedback:=cat("<math><mrow><mtext mathvariant='bold'>Your answer is incorrect. </mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer: </mtext><mtext>", StudentResponse, "</mtext><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, "<mtext mathvariant='bold'>Correct Answer: </mtext><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mfrac><mn>1</mn><mn>6</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mfrac><mrow><mi>x</mi><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mfenced open='(' close=')' separators=','><mrow><mn>8</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>45</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msqrt><mn>5</mn></msqrt><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msqrt><mrow><msup><mi>x</mi><mn>3</mn></msup></mrow></msqrt><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow></mrow></mfenced></mrow><mrow><msup><mi>y</mi><mn>2</mn></msup></mrow></mfrac></mrow></mrow></mrow></mstyle></math><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext>&NewLine;</mtext></mrow>", "`$RESPONSE`", StudentResponse)); feedback:=SubstituteAll(feedback, "`$ANSWER`", "<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>−</mo><mrow><mfrac><mn>1</mn><mn>6</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mfrac><mrow><mi>x</mi><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mfenced open='(' close=')' separators=','><mrow><mn>8</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mn>45</mn><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msqrt><mn>5</mn></msqrt><mo lspace='0.0em' rspace='0.0em'>⁢</mo><msqrt><mrow><msup><mi>x</mi><mn>3</mn></msup></mrow></msqrt><mo lspace='0.0em' rspace='0.0em'>⁢</mo><mi>x</mi></mrow></mrow></mfenced></mrow><mrow><msup><mi>y</mi><mn>2</mn></msup></mrow></mfrac></mrow></mrow></mrow></mstyle></math>"); feedback:=cat(feedback, "</mrow></math>"); fi; with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Feedback", [[MathMLViewer('value' = feedback, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): if feedback <> "" then Maplets[Display](maplet); fi;

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Resumo</Text-field>

Dado que 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 \303\251 definido implicitamente pela equa\303\247\303\243o 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, a deriva\303\247\303\243o impl\303\255cita \303\251 uma t\303\251cnica para 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 , a inclina\303\247\303\243o da reta tangente \303\240 curva. A chave para usar a deriva\303\247\303\243o impl\303\255cita com sucesso \303\251 lembrar que uma vari\303\241vel \303\251 definida implicitamente em termos da outra, usualmente 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, e que a deriva\303\247\303\243o em rela\303\247\303\243o a LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= de qualquer termo envolvendo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYjNidGMS1GOzYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y+RkBGQ0ZFRkdGSUZLRk0vRlBRJjAuMGVtRicvRlNGWi1GIzYnLUY7Ni1RIihGJ0Y+L0ZBRjZGQy9GRkY2RkdGSUZLRk0vRlBRLDAuMTY2NjY2N2VtRicvRlNGXm8tRiM2JC1GLDYlUSJ4RidGNEY3Rj4tRjs2LVEiKUYnRj5GW29GQ0Zcb0ZHRklGS0ZNRl1vL0ZTUSwwLjExMTExMTFlbUYnLUY7Ni1RIixGJ0Y+RkAvRkRGNkZFRkdGSUZLRk1GWS9GU1EsMC4zMzMzMzMzZW1GJ0Y+RitGPkYrRj5GK0Y+ envolver\303\241 automaticamente a Regra da Cadeia.

Uma express\303\243o para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtRiw2JVEjZHlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjtRJ25vcm1hbEYnLUYjNiQtRiw2JVEjZHhGJ0Y3RjpGPS8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGSS8lKWJldmVsbGVkR1EmZmFsc2VGJ0YrRj0= obtida pela deriva\303\247\303\243o impl\303\255cita envolver\303\241 tipicamente ambos, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Os Exemplos 14.1 e 14.2 demonstram como esta forma para a derivada pode ser usada efetivamente. O exemplo final estende a Regra de Pot\303\252ncia de expoentes inteiros para expoentes racionais. A deriva\303\247\303\243o impl\303\255cita ser\303\241 usada no Cap\303\255tulo 15 sobre Taxas Relacionadas.

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Pr\303\263ximo Cap\303\255tulo</Text-field>

Voc\303\252 agora conhece as t\303\251cnicas necess\303\241rias para derivar v\303\241rias classes de fun\303\247\303\265es. Voc\303\252 pode tamb\303\251m entender a conex\303\243o entre derivada, a taxa de varia\303\247\303\243o (instant\303\242nea) e a inclina\303\247\303\243o de uma reta tangente a uma curva. Usaremos posteriormente as id\303\251ias introduzidas nesta unidade em um n\303\272mero vasto de aplica\303\247\303\265es.

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