Calculus Archive: Questions from November 04, 2023
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Use implicit differentiation on the equation \( 2 e^{x y z}-2 x z^{2}+x \cos (y)=10 \) to find \( \frac{\partial z}{\partial x} \) and \( \frac{\partial z}{\partial y} \). \[ \begin{array}{ll} \frac{\1 answer -
limx→∞ 000 000 00 cr/co -00 0 1 3x3 - cos(9x) 5x2+16 =
\( \lim _{x \rightarrow \infty}\left(\frac{3 x^{3}-\cos (9 x)}{5 x^{2}+16}\right)= \)1 answer -
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Let \( y \) be the solution of IVP \( y^{\prime \prime \prime}+3 y^{\prime \prime}+3 y^{\prime}+y=0, y(0)=1, y^{\prime}(0)=0, y^{\prime \prime}(0)=1 \). Then \( y(-1)= \) a. \( -2 e \) b. e c. \( -e \1 answer -
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5 Given f(x,y) = x³ + 2xy³ + 4y², find fz(x, y) = fy(x, y) = 1 Question Help: Video Message instructor
Given \( f(x, y)=x^{5}+2 x y^{3}+4 y^{2} \), find \[ \begin{array}{l} f_{x}(x, y)= \\ f_{y}(x, y)= \end{array} \] Question Help: Video Message instructor1 answer -
If \( x y^{2}+e^{y}=x y \) (D) \( y^{\prime}=\frac{y^{2}-y}{x+2 x y+e^{y}} \) (E) None of the other choices (A) \( y^{\prime}=\frac{y^{2}-2 y}{2 x+2 x y-e^{y}} \) (B) \( y^{\prime}=\frac{y^{2}-y1 answer -
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Find the indicated limit by using the limits \( \lim _{(x, y) \rightarrow(a, b)} f(x, y)=2 \) and \( \lim _{(x, y) \rightarrow(a, b)} g(x, y)=2 \). \[ \lim _{(x, y) \rightarrow(a, b)} \frac{5 f(x, y)}1 answer -
Find the following limit. \[ \lim _{(x, y) \rightarrow(0,5)} \arctan \left(\frac{x^{2}+30}{x^{2}+(y-5)^{2}}\right) \] /2 Points] Find each limit. \[ f(x, y)=7 x^{2}+8 y^{2} \] (a) \( \lim _{\Delta x \1 answer -
Sea \( \Omega=\left\{(x, y, z) \in R^{3} \mid x^{2}+y^{2}+z^{2} \leq 1\right\} \) Encuentra \[ \int_{\Omega} d x d y d z \] a) Como una integral iterada. b) Escribe las integrales iteradas en 3 camino1 answer -
Sea \( f: J \rightarrow R \) con \( J \) un rectángulo en \( R^{n}, f \) integrable; y sea \( f=g \) excepto en un conjunto finito de puntos. a) Probar que \( g \) es integrable y que \[ \int_{J} f=\1 answer -
Find the derivative of y = ln y=[ Answer: y'= 4+5x2 x4
Find the derivative of \( y=\ln \left(\frac{\sqrt{4+5 x^{2}}}{x^{4}}\right) \). Answer: \( y^{\prime}= \)1 answer -
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Find each limit. \[ f(x, y)=2 x^{2}+9 y^{2} \] (a) \( \lim _{\Delta x \rightarrow 0} \frac{f(x+\Delta x, y)-f(x, y)}{\Delta x} \) (b) \( \lim _{\Delta y \rightarrow 0} \frac{f(x, y+\Delta y)-f(x, y)}{1 answer -
Find each limit. \[ f(x, y)=\frac{9}{x+y} \] (a) \( \lim _{\Delta x \rightarrow 0} \frac{f(x+\Delta x, y)-f(x, y)}{\Delta x} \) (b) \( \quad \lim _{\Delta y \rightarrow 0} \frac{f(x, y+\Delta y)-f(x,1 answer -
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2: If \( \iiint_{E} f(x, y, z) d V=\int_{0}^{\pi / 2} \int_{0}^{\pi / 4} \int_{0}^{\cos (\theta)} 9 \rho^{2} \sin (\phi) \cos (\phi) d \rho d \theta d \phi \), find \( f(x, y, z) \). \[ f(x, y, z)= \]1 answer -
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9. F(y) = 1 3 (-³) (y + 5y³)
9. \( F(y)=\left(\frac{1}{y^{2}}-\frac{3}{y^{4}}\right)\left(y+5 y^{3}\right) \)0 answers -
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Calculate the partial derivatives \( f_{x}(x, y) \) and \( f_{y}(x, y) \) \( f(x, y)=\sin (3 x) \cos (3 y) \)1 answer -
Calculate \( \mathrm{dz} / \mathrm{du} \) and \( \mathrm{dz} / \mathrm{dv} \) using the following functions. \[ \begin{array}{l} z=3 x^{2}-2 x y+y^{2} \\ x(u, y)=3 u+2 v \\ y(u, v)=4 u-v \end{array} \1 answer -
11) Mencione los primeros 10 términos de la secesión \( \left(a_{n}\right)_{n} \) definida por: \[ a_{1}=1, \text { y } a_{n}=\frac{(-1)^{n} a_{n-1}}{2} \forall n \geq 2 \text {. } \]1 answer -
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5. \( \iint_{R} x \sec ^{2} y d A ; R=\left\{(x, y): 0 \leq y \leq x^{2}, 0 \leq x \leq \sqrt{\pi} / 2\right\} \)1 answer -
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Express the integral \( \iiint_{E} f(x, y, z) d V \) as an iterated integral in six different ways, where \( \mathrm{E} \) is the solid bounded by \( z=0, x=0, z=y-2 x \) and \( y=4 \). 1. \( \int_{a}1 answer -
15) \( \left(\frac{n}{e^{n}}\right)_{n} \) ies creciente o decreciente? 16) \( \left(a_{n}\right)_{n} \) es una sucesión creciente si 17) \( \left(\frac{2 n+1}{n}\right)_{n} \), ¿es creciente o decr0 answers -
Evaluate the triple integral \( \iiint_{E} f(x, y, z) d V \) over the solid \( E \). \[ f(x, y, z)=x^{2}+y^{2}, E=\left\{(x, y, z) \mid x^{2}+y^{2} \leq 16, x \geq 0, x \leq y, 0 \leq z \leq 3\right\}1 answer -
the triple integral \( \iiint_{B} f(x, y, z) d V \) over the solid \( B \). \[ f(x, y, z)=1-\sqrt{x^{2}+y^{2}+z^{2}}, B=\left\{(x, y, z) \mid x^{2}+y^{2}+z^{2} \leq 9, y \geq 0, z \geq 0\right\} \]2 answers -
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