Calculus Archive: Questions from March 09, 2023
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Let \( g(x, y)=e^{x}+e^{2 y}+e^{3 x y^{2}} \). What is \( \frac{\partial g(x, y)}{\partial y} ? \) [a] \( e^{x}+2 e^{2 y}+6 x y e^{3 x y^{2}} \) [b] \( 2 e^{2 y}+6 x y e^{3 x y^{2}} \) [c] \( 2 e^{2 y2 answers -
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please help as soon as you can
Find the domain of the function: \[ \begin{array}{c} f(x, y)=x^{2} \ln \left(y-x^{2}\right)+2 \sqrt{3-y} \\ \left\{(x, y) \mid x^{2} \leq y, y \leq 3\right\} \\ \left\{(x, y) \mid x^{2}>y, y \geq 3\ri2 answers -
please answer
Considere la siguiente gráfica para hallar los límites en de su función según solicitado. 1) \( \lim _{x \rightarrow-2^{-}} f(x)= \) 2) \( \lim _{x \rightarrow-2^{+}} f(x)= \) 3) \( \lim _{x \righ2 answers -
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4. Find the solution to the IVP \[ y^{\prime \prime}+3 y^{\prime}=12 \cos (3 x) \begin{array}{c} y(0)=2 \\ y^{\prime}(0)=-2 \end{array} \]2 answers -
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Question 6. Find all absolute extrema on the given interval (a) \( y=\frac{1}{3} x^{3}-4 x,[-3,3] \). (b) \( y=3 x^{3 / 2}-2 x,[-1,1] \)2 answers -
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1. \( \lim _{x \rightarrow-4^{+}} \sqrt{4+2 x}= \) a. 0 c. \( -\infty \) b. \( \infty \) d. no definido 2. \( \lim _{x \rightarrow 0} \frac{4 x \sin x}{x^{2}}= \) a. \( \infty \) c. 4 b. -4 d. no defi2 answers -
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\( \begin{array}{l}I=\int_{c} F \\ F(x, y, z)=\left(2 x+y, x-4 y, y^{F_{1}+2}\right) \\ \therefore\left\{\begin{array}{l}x=x(t)=2 t+5 \\ y=y(t)=t^{2} \\ z=z(t)=t^{3}\end{array}\right.\end{array} \)2 answers -
s) Let \( g(x, y, z)=\frac{\cos \left(z^{3}\right) y^{2}}{x^{2}+1}+(4 x-1) y^{2} \), find \( g_{x}, g_{y} \), and \( g_{z} \).2 answers -
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Find all the second partial derivatives. \[ \begin{array}{l} \quad f(x, y)=x^{7} y^{5}+2 x^{4} y \\ f_{x x}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \\ f_{y y}(x, y)= \end{array} \]2 answers -
Helpp!
1) \( \lim _{x \rightarrow-2^{-}} f(x)= \) 2) \( \lim _{x \rightarrow-2^{+}} f(x)= \) 3) \( \lim _{x \rightarrow 0} f(x)= \) 4) \( \lim _{x \rightarrow 2} f(x)= \) 5) \( \lim _{x \rightarrow-2} f(x)=0 answers -
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EXPLAIN THE ANSWER.
8 The second order Taylor formula for the function \( f(x, y)=\cos (x y)+\sin y \) centered in \( \left(0, \frac{\pi}{2}\right) \) is \( \mathrm{A} f(x, y)=-\frac{\pi^{2}}{8} x^{2}-\frac{1}{2} y^{2}+\2 answers -
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please find the gradient of these function
5. \( f(x, y, z)=y z^{2} /\left(1+x^{2}\right) \) 6. \( f(x, y, z)=1 /\left(x^{2}+y^{2}+z^{2}\right) \) 7. \( f(x, y, z)=\sqrt{x^{2}+y^{2}+z^{2}} \) 8. \( f(x, y, z)=x e^{y} \sin z \)2 answers -
(1 point) Let \( F=(3 x+y) \exp (x+y), x=\ln (u) \), and \( y=v \). Find \( \frac{\partial F}{\partial u} \). Your answer should be in terms of \( x, y, u \), and \( v \). A. \( \frac{3 \exp (x+y)+(32 answers -
Evaluate the integral. \[ \begin{array}{l} \int \cos ^{4} 6 x d x \\ 3 x+\frac{1}{6} \sin 6 x+\frac{1}{12} \sin 24 x+C \\ \frac{3}{2} x+\frac{1}{6} \sin 12 x+\frac{1}{48} \sin 24 x+C \\ \frac{3}{2} x+2 answers -
\( y^{\prime \prime \prime}+4 y^{\prime \prime}+4 y^{\prime}=0 \) \( x^{2} y^{\prime \prime}+3 x y^{\prime}+10 y=0 \)2 answers -
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\( \begin{array}{l}\lim _{x \rightarrow 1}\left\{\left(4 x-x^{3}+2\right)+\frac{x^{2}-1}{x-1}\right\} \\ \lim _{t \rightarrow 4} \frac{\sqrt{t+5}-3}{t-4} \\ \lim _{h \rightarrow 0} \frac{\frac{1}{x+h}0 answers -
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Given \( f(x, y)=9 x^{4} y+2 x y^{3} \) \[ \begin{array}{c} \frac{\partial^{2} f}{\partial x^{2}}= \\ \frac{\partial^{2} f}{\partial y^{2}}= \end{array} \]2 answers -
La temperatura en el punto \( (x, y) \) es \( T(x, y) \), medida en grados Celsius. Un bicho se arrastra de tal manera que su posición después de \( t \) segundos está dada por \( : x=\sqrt{1+t}, \2 answers -
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Determine la derivada direccional de \[ f(x, y)=\sqrt{x y} \] en \( \mathrm{P}(2,8) \) en la dirección de \( \mathrm{Q}(5,4) \)2 answers -
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show all work
\( \int \frac{3 x^{4}-2 x+1}{x^{3}} d x \) \( \int\left(\sqrt{x}+\frac{6}{\sqrt[3]{x}}\right) d x \)2 answers -
Find the derivative. \[ y=7 x^{2} e^{-x} \] \( 7 x e^{x}(2-x) \) \( 7 x e^{-x}(x+2) \) \( 7 x e^{-x}(2-x) \) \( 14 x e^{-x}(1-x) \)2 answers -
Find the value of the integral \[ I=\iint_{A}\left(7 x^{2}-4 y^{2}\right) d x d y \] when \[ A=\{(x, y): 0 \leq y \leq 2 x, 0 \leq x \leq 1\} \]2 answers -
Suppose that \( f(x, y)=7 \), and \( D=\left\{(x, y) \mid x^{2}+y^{2} \leq 4\right\} \). \[ \iint_{D} f(x, y) d x d y= \]2 answers -
3. Determine the value of \( y \) when \( x=4 \). a) \( y=6 u^{2}-1, u=\sqrt{x} \) b) \( y=-\frac{5}{u^{3}}, u=9-2 x \)2 answers -
If \( f(x, y)=\ln \left(2 x y^{6}+7\right) \), find \( \frac{\partial f}{\partial x} \) and \( \frac{\partial f}{\partial y} \).2 answers -
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