Calculus Archive: Questions from July 24, 2023
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\( \begin{array}{l}f(x, y)=1+k x y \text { and } \\ \quad \iint_{R} f(x, y) d x d y=\iint_{R} f(x, y) d y d x=5 / 2\end{array} \)2 answers -
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3. Maximize the functions \( f(x, y, z)=x^{2}+2 y-z^{2} \) subject to the constraints. \[ g_{1}(x, y, z):=2 x-y=0 \quad g_{2}(x, y, z):=0 \]2 answers -
Integrate the function.
1) \( \int \frac{y^{2}}{\left(4-y^{2}\right)^{3 / 2}} d y \) A) \( \frac{y}{\sqrt{4-y^{2}}}+C \) B) \( \frac{2 y}{\sqrt{4-y^{2}}}-\sin ^{-1} y+C \) C) \( \frac{y}{\sqrt{4-y^{2}}}-\sin ^{-1}\left(\frac2 answers -
Find the values of the function. \[ f(x, y)=x^{2} /\left(1+y^{2}\right) \] (a) \( f(-8,0) \) (b) \( f(8,1) \) (c) \( f\left(\frac{1}{2},-\frac{1}{2}\right) \)2 answers -
Calculate the following. (a) \( \int_{1}^{2} \int_{0}^{3}(1+4 x y) d x d y \) (b) \( \int_{0}^{1} \int_{1}^{7} \frac{2 x e^{x}}{y} d y d x \) (c) \( \iint_{R}\left(18 x^{2} y^{3}-15 y^{4}\right) d A,2 answers -
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Find \( \frac{d^{2} y}{d x^{2}} \) for \[ y=19 x^{2} \cos (x)+1 \sin (x) \] \[ \frac{d^{2} y}{d x^{2}}= \]2 answers -
4 √ "* (e²² —- 72x) ª (e²¹² — 1) dx = 7x
\( \int_{0}^{4}\left(e^{7 x}-7 x\right)^{4}\left(e^{7 x}-1\right) d x= \)2 answers -
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