Calculus Archive: Questions from December 04, 2022
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Calculate \( \iint_{\mathcal{S}} f(x, y, z) d \sigma \) For \[ x^{2}+y^{2}=25, \quad 0 \leq z \leq 5 ; \quad f(x, y, z)=e^{-z} \] \[ \iint_{\mathcal{S}} f(x, y, z) d \sigma= \]2 answers -
2 answers
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Verify that \( z(x, y)=x \sin (y)+e^{x} \cos (y) \) satisfies the partial differential equation \( \frac{\partial^{2} z}{\partial x^{2}}+\frac{\partial^{2} z}{\partial y^{2}}+x \sin (y)=0 \) (5 marks)2 answers -
\( y=\frac{(3+x)(2-x)^{2}}{(4-3 x)^{3}} \), find the values of \( \mathrm{x} \) when \( \frac{d y}{d x}=0 \)2 answers -
PROBLEMA 2. Considere la función \( g(x)=\frac{x^{2}}{x^{2}+3} \) en el intervalo cerrado [-1, 1] para responder I, II, III, IV y \( V \). 1. Halle los numeros criticos. II. Halle los valores de \( x2 answers -
2 answers
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PROBLEMA 2. 2.4 out of te ouin Considere la función \( g(x)=\frac{x^{2}}{x^{2}+3} \) en el intervalo cerrado \( [-1,1] \) para responder \( \mathbf{I}, \mathbf{I I}, \mathbf{I I I} \), IV \( y \) V.2 answers -
2 answers
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Calculate ∬Sf(x,y,z)dS Fory=6−z2,0≤x,z≤8;f(x,y,z)=z∬Sf(x,y,z)dS=
Calculate \( \iint_{S} f(x, y, z) d S \) For \[ y=6-z^{2}, \quad 0 \leq x, z \leq 8 ; \quad f(x, y, z)=z \] \( \iint_{S} f(x, y, z) d S= \)2 answers -
draw the region and find its area
Dibuje la región y encuentre su área: \[ S=\left\{(x, y) / x \leq 1,0 \leq y \leq e^{x}\right\} \] Explique en sus propias palabras su procedimiento para resolver la integral impropia. Comparta sus2 answers -
Integrales Impropias
\[ S=\left\{(x, y) / x \leq 1,0 \leq y \leq e^{x}\right\} \] Explique en sus propias palabras su procedimiento para resolver la integral impropia. Comparta sus resultados con sus compañeros de clases2 answers -
1 answer
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Using L'Hopital Rule. Use a graphing calculator to find the limit. Find the limit analytically.
Considere el limite \( \lim _{x \rightarrow 0^{+}}(\cos x)^{1 / x^{2}} \) a. Use una calculadora gráfica para hallar el límite. b. Encuentre el límite analíticamente.2 answers -
2 answers
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\( y=\frac{5}{8} \) he derivative of \( y=\frac{3 x^{5}-7 x^{2}-4}{x^{2}} \) (x) if \( f(x)=6 x^{-2}+8 x^{3}+11 x \) \( \frac{d}{d x}\left(\frac{4}{x^{4}}-5 \sqrt[3]{x}\right) \)2 answers -
2 answers
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2 answers
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2 answers
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Consider the vector field. \[ \mathbf{F}(x, y, z)=\left\langle 4 e^{x} \sin y, 9 e^{y} \sin z, 7 e^{z} \sin x\right\rangle \] Find the curl of the vector field. curl \( \mathbf{F}= \)2 answers -
Solve the problem. Minimize \( Q=8 x^{2}+2 y^{2} \), where \( x+y=10 \) A) \( x=2 ; y=8 \) B) \( x=0 ; y=10 \) C) \( x=8 ; y=2 \) D) \( x=10 ; y=0 \)2 answers -
In Exercises \( 1 \square 6 \square \), find \( (a) \) the general solution and \( (b) \) the particular solution for the given initial condition. 1. \( y^{\prime}=5 x^{6} ; y(0)=-3 \) 2. \( y^{\prime2 answers -
2 answers
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pleas solve in detail
\( \nabla(x, y, z) \) eet,\( (x, y, z)=\frac{1}{\sqrt{x^{2}+y^{2}+z^{2}}} \) \( y(x, y, z) \) eet,\( (x, y, z)=\frac{1}{\sqrt{x^{2} y^{2}+z^{2}}} \) \( =\frac{\partial y}{\partial y} \varepsilon+\fra2 answers -
2 answers
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Find the following integral
Encuentre la siguiente integral: \[ \int_{0}^{2} \int_{0}^{1}\left(\frac{e^{\operatorname{Tan}^{-1}(x)}}{\left(x^{2}+1\right)^{\frac{3}{2}}}\right) y^{2} d x d y \]2 answers -
Given the following expression find:
2) Dada la siguiente expresión, encuentre \( \frac{\partial f}{\partial y} \) : \[ f(x, y)=e^{2 x}-e^{3 x y} \]2 answers -
Given the following expression Find af/ax and af/ay then evaluate f(2,2) in both cases
\[ f(x, y)=e^{x}+e^{y}+2 x^{2}+4 y+100 \] Encontrar \( \frac{\partial f}{\partial x} \) y \( \frac{\partial f}{\partial y} \) luego evalué \( f(2,2) \) en ambos casos2 answers -
ill in the blanks: \[ \begin{aligned} \int_{0}^{1} \int_{0}^{\frac{1-x}{2}} \int_{0}^{1-x-2 y} f(x, y, z) d z d y d x & =\bar{\int} \bar{\int} f(x, y, z) d y d z d x \\ & =\overline{[} \overline{[} \b2 answers -
2 answers
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Differentiate. \[ y=\ln \left[(x+6)^{2}(x+1)^{3}(x+3)^{6}\right] \] \[ \frac{d}{d x}\left[\ln \left[(x+6)^{2}(x+1)^{3}(x+3)^{6}\right]\right]= \] Find. \[ \frac{d^{2}}{d t^{2}}\left(t^{4} \ln t\right2 answers -
Find div(F × G) = ∇ · (F × G). F(x, y, z) = i + 5xj + 8yk G(x, y, z) = xi − yj + zk
\( \begin{aligned} \mathbf{i v}(\mathbf{F} \times \mathbf{G}) & =\nabla \cdot(\mathbf{F} \times \mathbf{G}) \\ \mathbf{F}(x, y, z) & =\mathbf{i}+5 x \mathbf{j}+8 y \mathbf{k} \\ \mathbf{G}(x, y, z) &2 answers -
Find curl(curl F) = ∇ × (∇ × F). F(x, y, z) = 4x3yzi + yj + 4zk
Find \( \operatorname{curl}(\mathbf{c u r l} \mathbf{F})=\nabla \times(\nabla \times \mathbf{F}) \). \( \mathbf{F}(x, y, z)=4 x^{3} y z \mathbf{i}+y \mathbf{j}+4 z \mathbf{k} \)2 answers -
/1 Points] SCALCET8 15.2.007. Evaluate the double integral. \[ \iint_{D} \frac{y}{x^{2}+1} d A, \quad D=\{(x, y) \mid 0 \leq x \leq 5,0 \leq y \leq \sqrt{x}\} \]2 answers -
2 answers
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Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For \[ y=3-z^{2}, \quad 0 \leq x, z \leq 5 ; \quad f(x, y, z)=z \] \[ \iint_{\mathcal{S}} f(x, y, z) d S= \]2 answers -
2 answers
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2 answers
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Evaluate \( \iiint_{E} 3 x z d V \) where \( E=\{(x, y, z) \mid 2 \leq x \leq 4, x \leq y \leq 2 x, 02 answers -
\( y=6 \ln \left(\frac{5}{x}\right) \) \( \frac{d y}{d x}= \) Differentiate the function \( y=\ln \left(8 x^{2}-9 x+8\right) \) \[ y^{\prime}= \]2 answers -
Find, r (t) for the following condition r'(t) = 4e2ti + 3e*j, r (0) = 2i Find, r"(t) of the following function r(t) = 4 cos t i + 4 without t j Determine the maximum height and horizontal displaceme
Resuelva: 1. Halle \( r(t) \) para la siguiente condición \( r^{\prime}(t)=4 e^{2 t} i+3 e^{t} j, r(0)=2 i \) 2. Halle \( r^{\prime \prime}(t) \) de la siguiente función \( r(t)=4 \cos t i+4 \sin t1 answer -
1. Let \( f(x)=2 x^{5} \sin (x) \) Find \( f^{\prime}(x) \) 2. Let \( y=x^{2} \cdot e^{x} \) a) Find \( y^{\prime} \) b) Find \( y^{\prime \prime} \)2 answers -
2 answers
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Solve the initial value problem. 13) \( \frac{d y}{d x}=4 x^{-3 / 4}, y(1)=5 \) A) \( y=16 x^{1 / 4}+80 \) B) \( y=4 x^{1 / 4}+1 \) C) \( y=-\frac{3}{4} x^{-7 / 4}-\frac{11}{4} \) D) \( y=16 x^{1 / 4}2 answers -
Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For \[ y=8-z^{2}, \quad 0 \leq x, z \leq 7 ; \quad f(x, y, z)=z \] \[ \iint_{\mathcal{S}} f(x, y, z) d S=\frac{2}{3}\left((197)^{\frac{3}{2}}-1\right2 answers -
Find the derivative. \[ \begin{array}{l} y=(2 x-1)^{3}(x+7)^{-3} \\ \frac{d y}{d x}=45(2 x-1)^{2}(x+7)^{-3} \\ \frac{d y}{d x}=45(2 x-1)^{2}(x+7)^{-4} \\ \frac{d y}{d x}=45(2 x-1)^{3}(x+7)^{-4} \\ \fr2 answers -
#45
(45) Find the integral \[ \int(5 x+1)^{2} d x \] (A) \( \frac{1}{3}(5 x+1)^{3}+C \) (B) \( (5 x+1)^{3}+C \) (C) \( \frac{1}{15}(5 x+1)^{3}+C \) (D) \( \frac{25}{3} x^{3}+x+C \)2 answers -
Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For \[ y=2-z^{2}, \quad 0 \leq x, z \leq 8 ; \quad f(x, y, z)=z \] \[ \iint_{\mathcal{S}} f(x, y, z) d S= \]2 answers -
Evaluate the triple integral. \[ \iiint_{E} y d V \text {, where } E=\{(x, y, z) \mid 0 \leq x \leq 7,0 \leq y \leq x, x-y \leq z \leq x+y\} \]2 answers -
Which of the following is a function \( f(x, y) \) such that \( \nabla f(x, y)=\langle y+\cos (y), x+2 y-x \sin (y)\rangle ? \) \[ \begin{array}{l} x y+y^{2}-x \cos y \\ x y-y^{2}-x \cos y-\pi x \\ x2 answers -
Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For \[ y=1-z^{2}, \quad 0 \leq x, z \leq 5 ; \quad f(x, y, z)=z \] \[ \iint_{\mathcal{S}} f(x, y, z) d S= \]2 answers -
Find the derivative of the function. \[ y=\frac{x^{2}-4}{(2 x-1)^{2}} \] A. \( y^{\prime}=-\frac{2 x-4}{(4 x-1)^{3}} \) B. \( y^{\prime}=-\frac{2 x}{(2 x-1)^{3}} \) C. \( y^{\prime}=\frac{2 x^{2}+16}{2 answers -
Find the derivative of the function. \[ y=\frac{x^{3}}{(x-1)^{3}} \] A. \( y^{\prime}=-\frac{3 x^{2}}{(x-1)^{4}} \) B. \( y^{\prime}=-\frac{3 x^{4}}{(x-1)^{3}} \) C. \( y^{\prime}=\frac{6 x^{2}}{(x-1)2 answers -
Find the derivative. \[ y=5 x^{2} e^{3 x} \] A. \( 10 e x^{3 x}(3 x+2) \) B. \( 10 x e^{3 x}(2 x+3) \) C. \( 5 x e^{3 x}(2 x+3) \) D. \( 5 x e^{3 x}(3 x+2) \)2 answers -
Solve the Initial value problem \[ 6 y^{\prime \prime}+y^{\prime}-y=0, y(0)=-1, y^{\prime}(0)=3 \] \[ y(x)= \]2 answers -
\[ \begin{array}{l} y=\frac{d y}{d x}:(30 \text { points }) \\ y=5 x^{2}+4 \sqrt{x}+\frac{13}{x^{2}}-e^{3} \end{array} \] \[ y=\left(1+x^{2}\right) \sec (x) \] \[ y=(\ln x)^{x}, x>0 \] d. \( y=\frac{e2 answers -
Find the derivative. \[ y=\frac{x^{2}+8 x+3}{\sqrt{x}} \] A. \( y^{\prime}=\frac{2 x+8}{x} \) B. \( y^{\prime}=\frac{3 x^{2}+8 x-3}{2 x^{3 / 2}} \) C. \( y^{\prime}=\frac{2 x+8}{2 x^{3 / 2}} \) D. \(2 answers -
Calculate \( \iint_{\mathcal{S}} f(x, y, z) d \sigma \) For \[ x^{2}+y^{2}=4, \quad 0 \leq z \leq 7 ; \quad f(x, y, z)=e^{-z} \]2 answers -
4. Triple integral \( 10 \mathrm{pts} \) Evaluate \( \int_{0}^{2} \int_{0}^{x} \int_{0}^{x+y} e^{x}(y+2 z) d z d y d x \)2 answers -
need help seeing if this converges or diverges
12. \( \sum_{n=0}^{\infty} \frac{2^{n} \cdot \sin ^{2}(5 n)}{4^{n}+\cos ^{2}(n)} \) \( =\lim _{n \rightarrow \infty} \frac{2^{n+1} \cdot \sin ^{2}(\operatorname{snn}+5)}{4^{n+1}+\cos ^{2}(n+1)}\left(\2 answers -
3). Compute all the critical points of the following functions. a. \( f(x, y)=10 x^{2}+6 y^{2}-5 x+3 y-18 \). b. \( g(x, y)=(x-13)^{2}+(y+15)^{2} \).2 answers -
1. Evaluate the definite integral. (a) \( \int_{0}^{\pi} \frac{\sin \theta+\sin \theta \tan ^{2} \theta}{\sec ^{2} \theta} d \theta \) (b) \( \int_{0}^{4}|2 x-5| d x \)2 answers -
(1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-15 y^{\prime \prime}+56 y^{\prime}=42 e^{x}, \] \[ y(0)=13, \quad y^{\prime}(0)=22, \quad y^{\prime \prime}(0)=27 . \] \(2 answers -
Find \( y^{\prime} \) if \( y=\sin x+\cos y \). (A) \( \frac{2 \cos x}{1+3 \sin y} \) \[ \frac{\cos x}{1+\sin y} \] (C) \( \frac{\cos x}{1+2 \sin y} \) \[ \ln (\ln y)+\ln y=\ln x \] \( \frac{y}{x+y}2 answers