Calculus Archive: Questions from July 27, 2022
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For \( f(x, y)=4 x^{3}+3 y-4 x^{2} y^{3} \), find the following (a) \( f_{x}(x, y) \) (b) \( f_{y}(x, y) \) (c) \( f_{x x}(x, y) \) (d) \( f_{x y}(x, y) \) (e) \( f_{y x}(x, y) \) (f) \( f_{y y}(x, y)1 answer -
Qi. Suppose Dy \( =N_{0} e^{k \tau} \) find 1) \( y= \) ? Q) if \( \tau=2 \) then, \( y= \) ? \( \# \)1 answer -
Evaluate the double integral over the given region. 2) \( \iint_{R} \sin 11 x d A \), R: \( 0 \leq x \leq \frac{\pi}{11}, 0 \leq y \leq \pi \)3 answers -
Calculate the iterated integral. \[ \int_{0}^{4} \int_{0}^{1}(x+y)^{2} d x d y \] Evaluate the double integral. \[ \iint_{D}(2 x+y) d A, \quad D=\{(x, y) \mid 1 \leq y \leq 5, y-4 \leq x \leq 4\} \]1 answer -
Question 15 (1 point) Evaluate \( \iint_{G} g(x, y, z) d S \). \( g(x, y, z)=z^{2} ; G: x^{2}+y^{2}+z^{2}=7, z \geq 0 \) A) \( \frac{49}{3} \pi \) B) \( \frac{98}{3} \pi \) C) \( 196 \pi \) D) \( \fra1 answer -
help please
Given \( y=\left(3 x^{2}+13 x+9\right) \cdot e^{x} \) find \( \frac{d y}{d x} \) \( \frac{d y}{d x}= \)1 answer -
1. Evaluate \( \iiint_{E} x y d V \), where \( E=\{(x, y, z) \mid 0 \leq x \leq 3,0 \leq y \leq x, 0 \leq z \leq x+y\} \). \[ \begin{array}{l} 0 \leq x \leq 3 \\ 0 \leq y \leq x \\ 0 \leq z \leq x+y \1 answer -
Evaluate the double integral. \[ \iint_{D} e^{-y^{2}} d A, \quad D=\{(x, y) \mid 0 \leq y \leq 5,0 \leq x \leq y\} \]1 answer -
Evaluate \( \iiint_{E} x y d V \), where \( E=\{(x, y, z) \mid 0 \leq x \leq 3,0 \leq y \leq x, 0 \leq z \leq x+y\} \).1 answer -
Determine \( f_{x} \) when 1. \( f_{x}=-x \sin (2 y-x) \) \( f(x, y)=x \sin (2 y-x)+\cos (2 y-x) \) 2. \( f_{x}=x \cos (2 y-x)-\sin (2 y-x) \) 3. \( f_{x}=x \cos (2 y-x) \) 4. \( f_{x}=-x \cos (2 y-x)1 answer -
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Determine \( h=h(x, y) \) so that \[ \frac{\partial f}{\partial x}=\frac{h(x, y)}{\left(4 x^{2}+5 y^{2}\right)^{2}} \] 1. \( h(x, y)=20 x^{3} y \) 2. \( h(x, y)=10 x y^{2} \) when \[ f(x, y)=\frac{2 x1 answer -
pts) If \( F(x, y, z)=\frac{x^{2}}{y+4 z} \), find \( \frac{\partial^{3} F}{\partial x^{2} \partial y} \)1 answer -
\( \lim _{x \rightarrow a} f(x)=777 \) \( \lim _{x \rightarrow a} \frac{\lim _{n \rightarrow \infty} \sum_{i=1}^{n} f\left(t_{i}\right)\left(\frac{x-a}{n}\right)}{x-a} \)3 answers -
\( \iint_{R}\left(5 x^{3} y^{2}-y^{2}\right) d A \quad R=\{(x, y) \mid 0 \leq x \leq 2,1 \leq y \leq 4\} \)1 answer -
\( \iint_{R}\left(5 x^{3} y^{2}-y^{2}\right) d A \quad R=\{(x, y) \mid 0 \leq x \leq 2,1 \leq y \leq 4\} \)1 answer -
Evaluate the double integral. \[ \iint_{D} 6 x \sqrt{y^{2}-x^{2}} d A, D=\{(x, y) \mid 0 \leq y \leq 4,0 \leq x \leq y\} \]1 answer -
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\( \int_{0}^{1} \int_{y}^{1} x y e^{x^{2}} d x d y \) \( \iint_{R} \frac{y}{3 x^{2}+1} d A \quad R=\{(x, y) \mid 0 \leq x \leq 1,-x \leq y \leq x\} \)3 answers -
Minimize \( Q=8 x^{2}+6 y^{2} \), where \( x+y=14 \) A. \( x=6 ; y=8 \) B. \( x=14 ; y=0 \) C. \( x=0 ; y=14 \) D. \( x=8 ; y=6 \)1 answer -
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