Calculus Archive: Questions from July 31, 2022
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3 answers
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3 answers
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Find the partial derivatives of \( f(x, y)=5 x^{3} y^{2} \). (a) \( f_{x}(x, y)= \) (b) \( f_{y}(x, y)= \) (c) \( f_{x}(2, y)= \) (d) \( f_{x}(x, 4)= \) (e) \( f_{y}(2, y)= \) (d) \( \quad f_{x}(x, 41 answer -
please help, I will upvote
Given \( f(x, y)=-2 x^{5}+6 x^{2} y^{6}+1 y^{4} \) \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y y}(x, y)= \] \[ f_{y x}(x, y)= \]1 answer -
1 answer
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\( y=-\frac{8}{x}+6 \tan x \), find \( y^{\prime} \) \[ y^{\prime}=\frac{-8}{x^{2}}+6 \sec ^{2} x \] \( y^{\prime}=-\frac{8}{x^{2}}+6 \tan ^{2} x \) \( y^{\prime}=\frac{-8}{x^{2}}-6 \csc x \) \( y^{\p1 answer -
1 answer
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If \( f(x, y)=x^{3} y+8 x y^{4} \), find the fo \[ \left.\frac{\partial^{2}}{\partial x^{2}} f(x, y)\right|_{(-1,1)}= \]1 answer -
1 answer
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partial derivatives1
Given \( f(x, y)=-3 x^{6}+5 x y^{5}+3 y^{4} \) \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \]3 answers -
given
Given \( f(x, y)=6 x^{2}-4 x y^{3}-y^{5} \), find the following numerical values: \[ \begin{array}{l} f_{x}(2,2)= \\ f_{y}(2,2)= \end{array} \]1 answer -
find the 1st partials
Find the 1st partials of \( f(x, y)=6 y e^{11 x y} \) \[ \begin{array}{l} f_{x}(x, y) \\ f_{y}(x, y) \\ f_{x x}(x, y) \\ f_{y y}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y) \end{array} \]1 answer -
1 answer
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given f(x,y)
Given \( f(x, y)=4 x^{5}-x^{2} y^{6}+6 y^{4} \) \[ f_{x}(x, y)= \] \( f_{y}(x, y)= \) \( f_{x x}(x, y)= \) \( f_{x y}(x, y)= \)3 answers -
optimization
Given \( f(x, y)=4 x^{3}-3 x y^{6}+3 y^{5} \) \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \]1 answer -
3 answers
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Problem. 8 : Find the flux of \( \mathbf{F} \) across the unit sphere \( x^{2}+y^{2}+z^{2}=1 \) if \[ \begin{array}{l} \mathbf{F}(x, y, z)=8 z \mathbf{i}+4 y \mathbf{j}+9 x \mathbf{k} . \\ \text { Flu3 answers -
Which of the following functions is continuous at \( (0,0) \) ? (i) \( f(x, y)=\left\{\begin{array}{ll}\frac{x y^{7}}{x^{8}+3 y^{8}} & \text { if }(x, y) \neq(0,0) \\ 0 & \text { if }(x, y)=(0,0)\end{1 answer -
1 answer
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Given the formula \( \int u^{\prime} e^{u} d x=e^{u}+c \), find three different \( f(x) \). So we can apply the formula to \( \int f(x) e^{x^{a}} d x \). (a is an integer) (15 points)1 answer -
1 answer
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\[ \begin{array}{c} \boldsymbol{F}(x, y, z)=\left(x, x y^{2}, x z\right) \\ \operatorname{div} \boldsymbol{F}=2 x y+x+1 \\ \operatorname{rot} \boldsymbol{F}=\left(0,-z, y^{2}\right) \end{array} \] \(1 answer -
3 answers