Calculus Archive: Questions from November 06, 2022
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No.9 Pls
In exercises 1-12, locate all critical points and classify them using Theorem 7.2. 1. \( f(x, y)=e^{-x^{2}}\left(y^{2}+1\right) \) 2. \( f(x, y)=\cos ^{2} x+y^{2} \) 3. \( f(x, y)=x^{3}-3 x y+y^{3} \)2 answers -
The domain of definition of \( f(x, y)=\frac{\ln (y-x)}{\sqrt{x^{2}+y^{2}-1}} \) is \( D=\left\{(x, y) \mid y>x\right. \) and \( \left.x^{2}+y^{2}>1\right\} \) \( D=\left\{(x, y) \mid y1\right\} \) N2 answers -
Let \( y(t) \) be the solution of \( y^{\prime \prime}+y=\delta(t-2 \pi)+\delta(t-4 \pi)=0, y(0)=1, y^{\prime}(0)=0 \). Then \( y\left(\frac{5 \pi}{2}\right)=\ldots . . \). 1 \( -1 \) \( 0.5 \) 02 answers -
2 answers
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(1 point) Integrate: \[ \int_{1}^{e^{7}} \int_{1}^{e^{1}} \int_{1}^{e^{5}} \frac{d x d y d z}{x y z} \]2 answers -
Find the differential \( d y \), given: (a) \( y=-x\left(x^{2}+3\right) \) (b) \( y=(x-8)(7 x+5) \) (c) \( y=\frac{x}{x^{2}+1} \)2 answers -
2. For each \( F(x, y)=0 \) use the implicit-function rule to find \( d y / d x \) : (a) \( F(x, y)=3 x^{2}+2 x y+4 y^{3}=0 \) (b) \( F(x, y)=12 x^{5}-2 y=0 \) (c) \( F(x, y)=7 x^{2}+2 x y^{2}+9 y^{4}2 answers -
(1 point) Let \( f(x, y, z)=\frac{x^{2}-5 y^{2}}{y^{2}+2 z^{2}} \). \( f_{x}(x, y, z) \) \( f_{y}(x, y, z) \) \( f_{z}(x, y, z)= \)2 answers -
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2 answers
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Evaluate the double integral. \[ \iint_{D}(2 x+y) d A, \quad D=\{(x, y) \mid 1 \leq y \leq 2, y-1 \leq x \leq 1\} \]2 answers -
2 answers
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show all work
If \( g(x, y)=x \sin (y)+y \sin (x) \) (a) \( g(\pi, 0) \) (b) \( 9\left(\frac{\pi}{2}, \frac{\pi}{3}\right) \) (c) \( g(0, y) \) (d) \( g(x, y+h) \)2 answers -
\( \frac{\tan \frac{17 \pi}{12}-\tan \frac{\pi}{12}}{1+\tan \frac{17 \pi}{12} \tan \frac{\pi}{12}}= \)2 answers -
If \( g(x, y)=x \sin (y)+y \sin (x) \), find the following. (a) \( g(\pi, 0) \) (b) \( g\left(\frac{\pi}{2}, \frac{\pi}{3}\right) \) \( \frac{\sqrt{3}}{2} \) (c) \( g(0, y) \) (d) \( g(x, y+h) \)2 answers -
Evaluate the triple integral. \[ \iiint_{E} y d V, \text { where } E=\{(x, y, z) \mid 0 \leq x \leq 6,0 \leq y \leq x, x-y \leq z \leq x+y\} \]2 answers -
Para la elaboración de un producto se tienen dos recipientes no marcados. Un recipiente contiene 17 onzas y el otro 55 onzas. Explicar cómo puede usarse los dos recipientes para medir exactamente un2 answers -
(1 point) Calculate all four second-order partial derivatives of \( f(x, y)=\sin \left(\frac{3 x}{y}\right) \). \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y) \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y)= \]2 answers -
2 answers
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2 answers
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Evaluate the triple integral. \[ \iiint_{E} y d V \text {, where } E=\{(x, y, z) \mid 0 \leq x \leq 4,0 \leq y \leq x, x-y \leq z \leq x+y\} \]2 answers -
Evaluate each integral. \[ \begin{array}{r} \int_{x-y}^{x+y} y d z= \\ \int_{0}^{x} \int_{x-y}^{x+y} y d z d y= \end{array} \] Now evaluate \( \iiint_{E} y d V \), where \( E=\{(x, y, z) \mid 0 \leq x2 answers -
Solve parts a and b. show all work
Consider the function \( y=e^{4-3 x} \) Find \( y^{\prime} \). Consider the function \( y=\frac{1}{e^{4 x}} \). Find \( y^{\prime} \)2 answers -
Solve parts a and b. show all work
Consider the function \( y=e^{4-3 x} \) Find \( y^{\prime} \). Consider the function \( y=\frac{1}{e^{4 x}} \). Find \( y^{\prime} \)2 answers -
Evaluate the triple integral \( \iiint_{B} f(x, y, z) d V \) over the solid \( B \). \[ f(x, y, z)=1-\sqrt{x^{2}+y^{2}+z^{2}}, B=\left\{(x, y, z) \mid x^{2}+y^{2}+z^{2} \leq 25, y \geq 0, z \geq 0\rig2 answers -
Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ y=\ln (1+\ln (x)) \] \[ y^{\prime}= \] \[ y^{\prime \prime}= \]2 answers -
( 1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-4 y^{\prime \prime}-y^{\prime}+4 y=0 \] \[ \begin{array}{l} y(0)=-8, \quad y^{\prime}(0)=0, \quad y^{\prime \prime}(0)=-2 answers -
Given \( f(x, y, z)=\sqrt{3 x^{2}+5 y^{2}+4 z^{2}} \), find \[ f_{x}(x, y, z)= \] \[ f_{y}(x, y, z)= \] \[ f_{z}(x, y, z)= \]2 answers -
Given \( f(x, y)=6 x^{5}-5 x y^{3} \), find \[ \begin{array}{l} f_{x x}(x, y)= \\ f_{x y}(x, y)= \\ f_{y y}(x, y)= \end{array} \]2 answers -
Given \( f(x, y, z)=\sqrt{6 x^{2}+2 y^{2}+z^{2}}, \mathrm{f} \) \( f_{x}(x, y, z)= \) \[ f_{y}(x, y, z)= \] \[ f_{z}(x, y, z)= \]2 answers -
2 answers
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Please answer i,m,n,o using the operator method. Please answer all.
4. Solve problems (a)-(g) using the method of undetermined coefficients. Solve all problems using the operator method. (a) \( y^{\prime \prime}+3 y^{\prime}-10 y=6 e^{4 x} \) (b) \( y^{\prime \prime}+2 answers -
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Suppose \( z=x^{2} \sin (y), x=-2 s^{2}-t^{2}, y=-6 s t \) A. Use the chain rule to find \( \frac{\partial z}{\partial s} \) and \( \frac{\partial z}{\partial t} \) as functions of \( x, y, s \) and \2 answers