Calculus Archive: Questions from December 16, 2023
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\( \begin{array}{l}\int_{0}^{83} \int_{x}^{\sqrt{166 x-x^{2}}} 9 \sqrt{x^{2}+y^{2}} d y d x= \\ (571787(-4+3 \pi)) / 2\end{array} \)1 answer -
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( int_{0}^{43} int_{x}^{sqrt{86 x-x^{2}}} 9 sqrt{x^{2}+y^{2}} d y d x= )
\( \int_{0}^{43} \int_{x}^{\sqrt{86 x-x^{2}}} 9 \sqrt{x^{2}+y^{2}} d y d x= \)1 answer -
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is this a linear differential equation ?
(f) \( y^{\prime \prime}+y=\left\{\begin{aligned} 1, & y>0 \\ -1, & y \leq 0\end{aligned}\right. \)1 answer -
Given \( f(x, y)=x^{6}+2 x^{2} y^{2}+4 y^{3} \) \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \]1 answer -
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( egin{array}{l}sin ^{-1}(infty)=cdots \ cos ^{-1}(infty)=cdots \ an ^{-1}(infty)=ldotsend{array} )
\( \begin{array}{l}\sin ^{-1}(\infty)=\cdots \\ \cos ^{-1}(\infty)=\cdots \\ \tan ^{-1}(\infty)=\cdots\end{array} \)1 answer -
( lim _{x ightarrow 0+}left(x-sqrt{x^{2}+x} ight) )
\( \lim _{x \rightarrow 0^{+}}\left(x-\sqrt{x^{2}+x}\right) \)1 answer -
\( \begin{array}{l}\lim _{x \rightarrow 0} \frac{\sin x-x}{\tan x-x} \\ \lim _{x \rightarrow 0} \frac{x-\sin x}{x^{3}}\end{array} \)1 answer