Calculus Archive: Questions from December 06, 2022
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2 answers
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2 answers
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P2 (cont.) b. \( y^{\prime \prime}+2 y^{\prime}+2 y=0 \) \( y(0)=3, \quad y^{\prime}(0)=2 \) c. \( y^{\prime \prime}+4 y^{\prime}+3 y=4 e^{-x} \quad y(0)=2, \quad y(0)=4 \)0 answers -
help
Find \( \frac{d y}{d x} \) where \( x y=\cos y \) \[ \begin{array}{l} y^{\prime}=-\frac{\sin y+y}{x} \\ y^{\prime}=-\frac{y}{x+\sin y} \\ y^{\prime}=-\frac{x \sin y+\cos y}{x^{2}} \\ y^{\prime}=\frac{2 answers -
#17,#22,#36
In Exercises 9-22, write the function in the form \( y=f(u) \) and \( u=g(x) \). Then find \( d y / d x \) as a function of \( x \). 9. \( y=(2 x+1)^{5} \) 10. \( y=(4-3 x)^{9} \) 11. \( y=\left(1-\fr2 answers -
Evaluate the Integral \[ \int(\sin \theta)\left(\csc ^{3} \theta-\csc ^{2} \theta-\tan \theta \sec \theta\right) d \theta \]2 answers -
Given \( f(x, y)=x^{3} y^{2}+3 x e^{y} \), find \( f_{y}(x, y) \). A. \( f_{y}(x, y)=6 x^{2} y+3 e^{y} \) B. \( f_{y}(x, y)=3 x^{2} y^{2}+3 e^{y}+2 x^{3} y+3 x e^{y} \) C. \( f_{y}(x, y)=6 x y^{2}+3 e2 answers -
Given \( f(x, y)=5 x^{2}-9 x y+2 y^{2} \), find \( f_{x}(x, y) \). A. \( f_{x}(x, y)=5 x-9 y \) B. \( f_{x}(x, y)=5 y-9 x \) C. \( f_{x}(x, y)=10 x-9 x y \) D. \( f_{x}(x, y)=10 x-9 \) E. \( f_{x}(x,2 answers -
Given \( f(x, y)=\left(5 x^{2}-2 y^{3}\right)^{7} \), find \( f_{x}(x \) A. \( f_{x}(x, y)=21 y^{2}\left(5 x^{2}-2 y^{3}\right)^{6} \) B. \( f_{x}(x, y)=70 x\left(5 x^{2}-2 y^{3}\right)^{6} \) C. \( f2 answers -
evaluate the integrals
\( \int(\sin \theta)\left(\operatorname{ssc}^{3} \theta-\csc ^{2} \theta-\tan \theta \sec \theta\right) d \theta \mid \) \( \int \frac{x^{8}}{\left(x^{3}+3\right)^{2}} d x \) \( \int \frac{3-x}{\sqrt{2 answers -
\( \int(\sin \theta)\left(\csc ^{3} \theta-\csc ^{2} \theta-\tan \theta \sec \theta\right) d \theta \)2 answers -
Let \( F(x, y, z)=\left(-2 x z^{2},-x y z,-4 x y^{3} z\right) \) be a vector field and \( f(x, y, z)=x^{3} y^{2} z \). \( \nabla f=( \) \( \nabla \times F=( \) \( F \times \nabla f=( \) \( F \cdot \na2 answers -
Parte I: Calcular el limite de las siguientes funciones e indicar si existe o no 1. \( \lim _{(x, y) \rightarrow(1,1)} \frac{x y}{x^{2}+y^{2}} \) 2. \( \lim _{(x, y) \rightarrow(0,0)} \frac{x^{2}}{\le2 answers -
Parte II: Calcular el limite y analizar la continuidad de la función 1. \( \lim _{(x, y) \rightarrow(2,1)} 2 x^{2}+y \) 2. \( \lim _{(x, y) \rightarrow(0,0)} x+4 y+1 \) 3. \( \lim _{(x, y) \rightarro2 answers -
18 please ASAP!
Find curl \( (\mathbf{F} \times \mathbf{G}) \). \[ \begin{array}{l} \mathbf{F}(x, y, z)=7 \mathbf{i}+8 x \mathbf{j}+9 y \mathbf{k} \\ \mathbf{G}(\mathrm{x}, \mathrm{y}, \mathrm{z})=7 \mathrm{x} \mathb2 answers -
Compute the gradient vector fields of the following functions: A. \( f(x, y)=9 x^{2}+10 y^{2} \) \( \nabla f(x, y)=\quad \) i+ \( \quad \mathbf{j} \) B. \( f(x, y)=x^{2} y^{7} \) \( \nabla f(x, y)=\qu2 answers -
*11. Evaluate the integral. \[ \int 2 \cos ^{4} 6 x d x \] A. \( \frac{3}{2} x+\frac{1}{12} \sin 6 x+\frac{1}{24} \sin 24 x+C \) B. \( \frac{3}{4} x+\frac{1}{12} \sin 12 x+\frac{1}{96} \sin 24 x+C \)2 answers -
2 answers
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\( f(x)=e^{\sin \left(3 x^{2}\right)} \), then \( f^{\prime}(x)= \) \( e^{\sin \left(3 x^{2}\right)} \cos \left(3 x^{2}\right) \) \( e^{\cos \left(3 x^{2}\right)} \cos \left(3 x^{2}\right) \) \( 6 x e2 answers -
2 answers
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(1 point) Let \( f(x, y, z)=\frac{x^{2}-4 y^{2}}{y^{2}+3 z^{2}} \). \[ \begin{array}{l} f_{x}(x, y, z)= \\ f_{y}(x, y, z)= \\ f_{z}(x, y, z)= \end{array} \]2 answers -
Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For Part of the surface \( x=z^{3} \), where \( 0 \leq x, y \leq 13^{-\frac{3}{2}} ; \quad f(x, y, z)=x \) \[ \iint_{\mathcal{S}} f(x, y, z) d S= \]2 answers -
4.3 #4
Given \( f(x, y, z)=\sqrt{5 x^{2}+y^{2}+3 z^{2}} \) \[ f_{x}(x, y, z)= \] \[ f_{y}(x, y, z)= \] \[ f_{z}(x, y, z)= \]2 answers -
Find the spherical coordinate expression for the function \( F(x, y, z) \). \[ \begin{array}{l} F(x, y, z)=x^{3} y^{3} \sqrt{x^{2}+y^{2}+z^{2}} \\ f(\rho, \theta, \varphi)= \\ \end{array} \]2 answers -
1. Si se sabe que 2 es una raíz de multiplicidad doble y que \( 2-i \) es también una raíz de la ecuación auxiliar de una ecuación diferencial, que tiene coeficientes constantes CauchyEuler, ¿cu2 answers -
2. El radio de convergencia de la serie \( \sum_{k=0}^{\infty} \frac{1}{k^{2}+k}(3 x-1)^{k} \) es: a) \( R=0 \) b) \( R=1 / 3 \) c) \( R=1 \) d) \( R=3 \) e) Ninguna de las Anteriores2 answers -
2 answers
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Halla la solución del sistema \[ \begin{aligned} D x+\quad D y & =e^{t} \\ -D^{2} x+D x+x+y & =0 \end{aligned} \]1 answer -
Calculate \( \iint_{S} f(x, y, z) d S \) For \[ y=1-z^{2}, \quad 0 \leq x, z \leq 9 ; \quad f(x, y, z)=z \] \( \iint_{S} f(x, y, z) d S= \)2 answers -
2 answers
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[10 pts.] Halla dos soluciones en series de potencias alrededor de \( x=0 \) para la ecuación diferencial \( y^{\prime \prime}-x^{2} y=0 \).2 answers -
1. Si \( y_{1}, y_{2} \) son dos soluciones de una ecuación diferencial de segundo orden \( \mathrm{y} \) el \( W\left(y_{1}, y_{2}\right)=0 \), entonces las soluciones son linealmente dependientes.2 answers -
Which of the following expressions is \( y^{\prime} \) if \( y=\cos \left(\frac{x}{x-1}\right) ? \) A. \( y^{\prime}=-\frac{(2 x-1)}{(x-1)^{2}} \sin \left(\frac{x}{x-1}\right) \) B. \( y^{\prime}=\fra2 answers -
Thank you!
Which of the following expressions represents \( y^{\prime} \) when \( y=e^{\sin ^{2} x} ? \) A. \( y^{\prime}=e^{2 \sin x \cos x} \) B. \( y^{\prime}=\left(e^{\sin ^{2} x}\right) \sin x \cos x \) C.2 answers -
Given \( f(x, y)=-6 x^{5}-5 x^{2} y^{4}+2 y^{2} \) \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \]2 answers -
2 answers
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Let \( f(x, y, z)=2 x z e^{5 y z} \). Find \( \frac{\partial f}{\partial x}(x, y, z), \frac{\partial f}{\partial y}(x, y, z) \), and \( \frac{\partial f}{\partial z}(x, y, z) \).2 answers -
Please explain how to get to that point.
Find \( \frac{d y}{d x} \) when \[ \tan (x-y)=4 x+2 y . \] 1. \( \frac{d y}{d x}=\frac{2-\sec ^{2}(x-y)}{\sec ^{2}(x-y)+4} \) 2. \( \frac{d y}{d x}=\frac{2+\sec ^{2}(x-y)}{\sec ^{2}(x-y)+4} \) 3. \( \2 answers -
Solve the system of equation
4 [10 puntos] Resuelva el sistema de ecuaciones diferenciales de primer orden \[ \left\{\begin{array}{c} x^{\prime}=-y+t \\ y^{\prime}=x-t \end{array}\right. \]2 answers -
solve the integral equation
6 [10 puntos] Resuelva la ecuación integral \( y(t)+\int_{0}^{t} y(v) d v=1 \)2 answers -
\( \begin{aligned} \operatorname{curl}(\mathbf{F} \times \mathbf{G}) & =\nabla \times(\mathbf{F} \times \mathbf{G}) \\ \mathbf{F}(x, y, z) & =\mathbf{i}+9 x \mathbf{j}+5 y \mathbf{k} \\ \mathbf{G}(x,2 answers -
\( \begin{aligned} \operatorname{curl}(\text { curl F }) & =\nabla \times(\nabla \times \mathbf{F}) \\ \mathbf{F}(x, y, z) & =3 x^{3} y z \mathbf{i}+y \mathbf{j}+3 z \mathbf{k}\end{aligned} \)2 answers -
Evaluate the following integral. \[ \int 11 \sin ^{3} x \cos ^{2} x d x \] \[ \int 11 \sin ^{3} x \cos ^{2} x d x= \]2 answers -
2 answers
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Part of the surface \( x=z^{3} \), where \( 0 \leq x, y \leq 13^{-\frac{3}{2}} ; \quad f(x, y, z)=x \) \[ \iint_{\mathcal{S}} f(x, y, z) d S= \]2 answers -
Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For \[ y=3-z^{2}, \quad 0 \leq x, z \leq 7 ; \quad f(x, y, z)=z \] \[ \iint_{\mathcal{S}} f(x, y, z) d S= \]2 answers -
Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For \[ x^{2}+y^{2}=25, \quad 0 \leq z \leq 4 ; \quad f(x, y, z)=e^{-z} \] \[ \iint_{\mathcal{S}} f(x, y, z) d S= \]2 answers -
Given \( f(x, y)=2 x^{3} \cos \left(y^{6}\right) \), find \[ \begin{array}{l} f_{x y}(x, y)=-36 x^{2} y^{5} \sin \left(y^{6}\right) \\ f_{y y}(x, y)=-12 x^{3}\left(5 y^{4} \sin \left(y^{6}\right)+6 y^2 answers -
(b) \( \int \frac{3 x-1}{x^{2}+8 x+21} d x \) (c) \( \int \frac{\sin x+\cos x}{\sqrt{\sin x-\cos x}} \cdot 2^{\sqrt{\sin x-\cos x}} d x \)2 answers -
Evaluate the double integral \( \iint_{D} x^{2} d A \), where \( D=\{(x, y): 1 \leq x \leq e, 0 \leq y \leq \ln x\} \). Answer:2 answers -
Problem 2: Solve the initial value problem \[ \mathbf{y}^{\prime}=\left(\begin{array}{ll} 3 & 2 \\ 1 & 2 \end{array}\right) \mathbf{y}, \quad \mathbf{y}(0)=\left(\begin{array}{c} -1 \\ 1 \end{array}\r2 answers