Calculus Archive: Questions from July 18, 2022
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1 answer
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just need B & D, (the two red blank boxes)
\( \left(1\right. \) point) Let \( f(x, y)=\frac{4 x^{2}+1 y}{y^{2}+6} \) \[ \begin{array}{l} f_{x}(x, y)= \\ f_{y}(x, y)= \\ f_{x}(3,1)= \\ f_{y}(3,1)= \end{array} \]1 answer -
just need B&D, (the two red blank boxes)
\( \left(1\right. \) point) Let \( f(x, y)=4 x^{4} \cdot 2^{y} . \) \[ \begin{array}{l} f_{x}(x, y)= \\ f_{y}(x, y)= \\ f_{x}(2,2)= \\ f_{y}(2,2)= \end{array} \]1 answer -
just need D (red blank box)
(1 point) Let \( f(x, y)=y \ln \left(6+x^{2}\right)+2 y^{2} \) \[ \begin{array}{l} f_{x}(x, y)= \\ f_{y}(x, y)= \\ f_{x}(2,3)= \\ f_{y}(2,3)= \end{array} \]1 answer -
need B and D, (the red boxes
(1 point) Let \( f(x, y)=\frac{4 x^{2}+1 y}{y^{2}+6} \) \[ \begin{array}{c} f_{x}(x, y)= \\ f_{y}(x, y)= \\ f_{x}(3,1)= \\ f_{y}(3,1)= \end{array} \]3 answers -
Given \( f(x, y)=5 x^{5}+4 x^{2} y^{2}-y^{4}, \mathrm{fi} \) \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \]1 answer -
SHOW ALL WORK PLZ
Find all the second partial derivatives. \[ f(x, y)=x^{6} y-3 x^{5} y^{2} \] \( f_{x x}(x, y)= \) \( f_{x y}(x, y)= \) \( f_{y x}(x, y)= \) \( f_{y y}(x, y)= \)1 answer -
Find all the second partial derivatives. \[ f(x, y)=x^{6} y-2 x^{5} y^{2} \] \( f_{X x}(x, y)= \) \( f_{x y}(x, y)= \) \( f_{y x}(x, y)= \) \( f_{y y}(x, y)= \)1 answer -
1 answer
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1 answer
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Calculate all four second-order partial derivatives of \( f(x, y)=(3 x+4 y) e^{y} \). \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y)= \]1 answer -
1 answer
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\( \operatorname{Max} P=5 x+4 y \) Subject to: \[ \begin{array}{l} 8 x+2 y \geq 16 \\ 4 x+5 y \leq 20 \\ x \geq 0, y \geq 0 \end{array} \]1 answer -
4. Avaluate the triple integral. a) \( \iint_{E} \) \( \iint_{E} y d V \), where \( E=\{(x, y, z) \mid 0 \leq x \leq 3,0 \leq y \leq x, x-y \leq z \leq x+y\} \)1 answer -
\( I=\int 97 \frac{\cot ^{5}(\sqrt{x}) \csc ^{4}(\sqrt{x})}{\sqrt{x}} d x=a \int\left(u^{b}+u^{c}\right) d u \)3 answers -
Find the indicated derivative. Find \( y^{\prime \prime} \) if \( y=4 x \sin x \). \[ \begin{array}{l} y^{\prime \prime}=-8 \cos x+4 x \sin x \\ y^{\prime \prime}=4 \cos x-8 x \sin x \\ y^{\prime \pri1 answer -
(\#3) [4 pts.] If \( f(x, y, z)=\ln (x+y+z) \), then evaluate \( f_{x y z}(1,1,1) \). Show all algebra!1 answer -
Evaluate: \( \int \tan ^{\frac{3}{2}} y \sec ^{4} y d y \) A) None (3) \( \frac{2}{5} \tan ^{\frac{5}{2} y+C} \) (C) \( \frac{2}{5} \tan ^{\frac{5}{2}} y+\frac{2}{9} \tan ^{\frac{9}{2}}+C \) (D) \( \t1 answer -
Find the gradient of the function \( f(x, y)=x^{2} y+y^{3} \). \[ \begin{aligned} \nabla f(x, y) &=x \widehat{i}+\left(x+3 y^{2}\right) \widehat{j} \\ \nabla f(x, y) &=x y \widehat{i}+\left(x^{2}+3 y^3 answers -
1 answer
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\( \int \frac{e^{\ln \sec ^{2}(\sin 2 y)} d y}{\sec 2 y} \) can be evaluated as (A) \( \frac{1}{2} \int \sec ^{2}(\sin 2 y) \cdot 2 \cos 2 y d y \) (D) \( \int \sec ^{2}(\sin 2 y) \cdot 2 \cos 2 y d y1 answer -
(\#3) [4 pts.] If \( f(x, y, z)=\ln (x+y+z) \), then evaluate \( f_{x y z}(1,1,1) \). Show all algebra!1 answer -
A factory is discharging pollutants at a rate of 饾憛(饾憽) = 1000饾憯饾憥饾憴/饾憫ay. Using enzymes and other remedies, the survival function of the pollutants in the lake is 饾憜(饾憽) = 饾憭 ^-0.1t
4- [6 pts.] Una f谩brica est谩 descargando contaminantes a una raz贸n de \( R(t)=1000 \mathrm{gal} / \mathrm{dia} \). Utilizando enzimas \( \mathrm{y} \) otros remedios, la funci贸n de sobrevivencia d1 answer -
Determine the equilibrium points and the stability of the function given by the differential equation dN/dt=0.25N(1-N/10)-0.10N
5- [4 pts.] Determine los puntos de equilibrio y la estabilidad de la funci贸n dada por la ecuaci贸n diferencial \[ \frac{d N}{d t}=0.25 N\left(1-\frac{N}{10}\right)-0.10 N \]1 answer -
Determine the function that satisfies the differential equation dy/dx= x^4/y^4 and initial condition 饾懄(0) = 1.
6- [4 pts.]Determine la funci贸n que satisface la ecuaci贸n diferencial \( \frac{d y}{d x}=\frac{x^{4}}{y^{4}} \) y condici贸n inicial \( y(0)=1 \).1 answer -
Compute the partial derivatives 饾憮x , 饾憮y of the function 饾憮(饾懃, 饾懄) = cos^2(饾懃^2 + 3饾懃饾懄^2 + 4饾懄^4) .
7- [4 pts.]Compute las derivadas parciales \( f_{x}, f_{y} \) de la funci贸n \( f(x, y)=\cos ^{2}\left(x^{2}+3 x y^{2}+4 y^{4}\right) \).1 answer -
Find the derivative. \[ y=\operatorname{arcsech}\left(\sqrt{1-x^{2}}\right), x>0 \] \[ y^{\prime}= \]1 answer -
Find the domain of the function. \[ f(x, y, z)=\frac{x y z}{\sqrt{3 x^{2}+6 y^{2}+8 z^{2}}} \] The domain is \[ \begin{array}{ll} \{(x, y, z) \mid(x, y, z) \neq(0,0,0)\} & \{(x, y, z) \mid(x, y, z)=(01 answer -
Answer Bank \( z=f(x, y)=4 x^{2}+y^{2} \) \[ z=f(x, y)=\frac{x^{2}}{2^{2}}-\frac{y^{2}}{1^{2}} \] \( z=f(x, y)=\frac{x y\left(x^{2}-y^{2}\right)}{x^{2}+y^{2}} \) \( z=f(x, y)=2 x-y-2 \)1 answer -
1. 2.
\( y=\frac{2 x^{8}-3 x^{7}+5}{x^{5}} \) Find \( \frac{d y}{d x} \) if \( y=\frac{9 x-5}{45 x^{5}} \) \[ \frac{d y}{d x}= \]1 answer