A função composta , g(u(x,y),v(x,y)) , de g(x,y) =y sen(x²y),
se u(x,y) = x²y³ e v(x,y) = πxy , é :
a) g(u(x,y),v(x,y)) = πxy sen (x^5y^7 π)
b) g(u(x,y),v(x,y)) = πxy sen (x²y^4 π)
c) g(u(x,y),v(x,y)) = x²y³ sen (xyπ)
d) g(u(x,y),v(x,y) = x²y³ sen (x²y)
e) g(u(x,y),v(x,y) = πxy sen (x²y)
Soluções para a tarefa
Respondido por
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Boa tarde Roger!
Solução!
![go(u,v)\\\\\\
$g(u(x,y),v(x,y))$\\\\\\\
$u(x,y)=(x^{2}y^{3})$\\\\\\\
$V(x,y)=(\pi xy$)](https://tex.z-dn.net/?f=go%28u%2Cv%29%5C%5C%5C%5C%5C%5C%0A%24g%28u%28x%2Cy%29%2Cv%28x%2Cy%29%29%24%5C%5C%5C%5C%5C%5C%5C%0A%24u%28x%2Cy%29%3D%28x%5E%7B2%7Dy%5E%7B3%7D%29%24%5C%5C%5C%5C%5C%5C%5C%0A%24V%28x%2Cy%29%3D%28%5Cpi+xy%24%29%0A "go(u,v)\\\\\\
$g(u(x,y),v(x,y))$\\\\\\\
$u(x,y)=(x^{2}y^{3})$\\\\\\\
$V(x,y)=(\pi xy$)")
Fazendo!\\\\\\
![g((x^{2}y^{3}),\pi xy$) y)\\\\\\\
g(x^{2}y^{3},\pi xy)=ysen(x^{2},y)\\\\\\
g(x^{2}y^{3},\pi xy)=ysen((x^{2}y^{3},\pi xy)^{2}y)\\\\\\\
Multiplicando~~os~~expoentes!\\\\\\\
g(x^{2}y^{3},\pi xy)=ysen((x^{4}y^{6}\pi^{2} x^{2}y^{2} )y)\\\\\\\
Veja~~ que~~tem~~ y ~~multiplicando~~ em \\\\\\ambos~~ os~~ lados,vamos~~ passar ~~dividindo.\\\\\\
\dfrac{sen((x^{4}y^{6}\pi^{2} x^{2}y^{2} )y)}{y}\\\\\\
sen(x^{4}y^{6}\pi^{2} x^{2}y^{2})](https://tex.z-dn.net/?f=g%28%28x%5E%7B2%7Dy%5E%7B3%7D%29%2C%5Cpi+xy%24%29+y%29%5C%5C%5C%5C%5C%5C%5C%0Ag%28x%5E%7B2%7Dy%5E%7B3%7D%2C%5Cpi+xy%29%3Dysen%28x%5E%7B2%7D%2Cy%29%5C%5C%5C%5C%5C%5C%0Ag%28x%5E%7B2%7Dy%5E%7B3%7D%2C%5Cpi+xy%29%3Dysen%28%28x%5E%7B2%7Dy%5E%7B3%7D%2C%5Cpi+xy%29%5E%7B2%7Dy%29%5C%5C%5C%5C%5C%5C%5C%0AMultiplicando%7E%7Eos%7E%7Eexpoentes%21%5C%5C%5C%5C%5C%5C%5C%0Ag%28x%5E%7B2%7Dy%5E%7B3%7D%2C%5Cpi+xy%29%3Dysen%28%28x%5E%7B4%7Dy%5E%7B6%7D%5Cpi%5E%7B2%7D++x%5E%7B2%7Dy%5E%7B2%7D+%29y%29%5C%5C%5C%5C%5C%5C%5C%0AVeja%7E%7E+que%7E%7Etem%7E%7E+y+%7E%7Emultiplicando%7E%7E+em+%5C%5C%5C%5C%5C%5Cambos%7E%7E+os%7E%7E+lados%2Cvamos%7E%7E+passar+%7E%7Edividindo.%5C%5C%5C%5C%5C%5C%0A+%5Cdfrac%7Bsen%28%28x%5E%7B4%7Dy%5E%7B6%7D%5Cpi%5E%7B2%7D++x%5E%7B2%7Dy%5E%7B2%7D+%29y%29%7D%7By%7D%5C%5C%5C%5C%5C%5C%0Asen%28x%5E%7B4%7Dy%5E%7B6%7D%5Cpi%5E%7B2%7D++x%5E%7B2%7Dy%5E%7B2%7D%29%0A%0A%0A+ "g((x^{2}y^{3}),\pi xy$) y)\\\\\\\
g(x^{2}y^{3},\pi xy)=ysen(x^{2},y)\\\\\\
g(x^{2}y^{3},\pi xy)=ysen((x^{2}y^{3},\pi xy)^{2}y)\\\\\\\
Multiplicando~~os~~expoentes!\\\\\\\
g(x^{2}y^{3},\pi xy)=ysen((x^{4}y^{6}\pi^{2} x^{2}y^{2} )y)\\\\\\\
Veja~~ que~~tem~~ y ~~multiplicando~~ em \\\\\\ambos~~ os~~ lados,vamos~~ passar ~~dividindo.\\\\\\
\dfrac{sen((x^{4}y^{6}\pi^{2} x^{2}y^{2} )y)}{y}\\\\\\
sen(x^{4}y^{6}\pi^{2} x^{2}y^{2})")
![Agrupando~~os~~termos~~semelhantes!\\\\\
sen(x^{6}y^{8}\pi^{2} )\\\\\\\
Colocando~~em~~evidencia!\\\\\\
\boxed{\pi xy.sen( x^{5}y^{7} \pi )}](https://tex.z-dn.net/?f=Agrupando%7E%7Eos%7E%7Etermos%7E%7Esemelhantes%21%5C%5C%5C%5C%5C%0A++sen%28x%5E%7B6%7Dy%5E%7B8%7D%5Cpi%5E%7B2%7D+%29%5C%5C%5C%5C%5C%5C%5C%0AColocando%7E%7Eem%7E%7Eevidencia%21%5C%5C%5C%5C%5C%5C%0A+%5Cboxed%7B%5Cpi+xy.sen%28+x%5E%7B5%7Dy%5E%7B7%7D+%5Cpi+%29%7D++ "Agrupando~~os~~termos~~semelhantes!\\\\\
sen(x^{6}y^{8}\pi^{2} )\\\\\\\
Colocando~~em~~evidencia!\\\\\\
\boxed{\pi xy.sen( x^{5}y^{7} \pi )}")
Boa tarde!
Bons estudos!
Solução!
Fazendo!\\\\\\
Boa tarde!
Bons estudos!
Usuário anônimo:
Qualquer dúvida é só mandar uma mensagem.
Muito obrigado amigo ^^ !
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