Calculus Archive: Questions from October 26, 2023
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Find \( \frac{\partial z}{\partial u} \) when \( u=0, v=2 \), if \( z=\sin (x y)+x \sin (y), x=2 u^{2}+2 v^{2} \), and \( y=u v \). \( \left.\frac{\partial z}{\partial u}\right|_{u=0, v=2}= \) (Simpli1 answer -
Find d 1+ sec x dx sin x sin x a O cos²x - COS X ? sin x .b O COS X CO sin ²x
\( \begin{array}{r}\frac{d}{d x}\left(\frac{1+\sec x}{\sin x}\right) \\ \frac{\sin x}{\cos ^{2} x} \\ \frac{\cos x}{\sin x} \\ -\frac{\cos x}{\sin ^{2} x}\end{array} \)1 answer -
Calculate all four second-order partial derivatives of f(x, y) = sin (2) fxx (x, y) = sin y fry (x, y) = fyr (x, y) = = fyy (x, y) =
Calculate all four second-order partial derivatives of \( f(x, y)=\sin \left(\frac{2 x}{y}\right) \) \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y)= \]1 answer -
Un hormiguero tiene la forma que se logra al girar la región acotada por \( y=1-x^{2} \) y el eje \( x \) alrededor del eje \( y \). Un investigador quita una parte cilíndrica del centro del hormigu1 answer -
Encuentre \( t \) de manera que el área entre \( y=\frac{2}{x+1} \) y \( y=\frac{2 x}{x^{2}+1} \) ea igual a \( \ln \left(\frac{3}{2}\right) \) para \( x \in[0, t] \).1 answer -
3. La función gamma \( \Gamma(\alpha)=\int_{0}^{\infty} t^{\alpha-1} e^{-t} d t, t>0 \). Demuestre que \( \Gamma(\alpha+1)=\alpha \Gamma(\alpha) \).1 answer -
3. (20 points) Determine the extreme values of the function \( F(x, y)=x^{2}+y \) on the ellipse \( 4 x^{2}+9 y^{2}=36 \). (Subject to \( G(x, y)=4 x^{2}+9 y^{2}=36 \).)1 answer -
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3. Hallar un vector unitario y ortogonal a los vectores \( \vec{A}=i-4 j+k, \vec{B}=2 i+3 j \) \[ \begin{array}{l} -\frac{\sqrt{3}}{\sqrt{134}} i+\frac{2}{\sqrt{134}} j+\frac{11}{\sqrt{134}} k \\ -\fr0 answers -
Si \( r(x)=x^{2} i+x \cos (\pi x) j+\operatorname{sen}(\pi x) k \) : a. \( \int_{0}^{2} \mathrm{r}(\mathrm{x})= \) \[ \mathbf{r}^{\prime}(5)= \]1 answer -
4. Si \( \mathrm{f}(\mathrm{x}, \mathrm{y})=\frac{\sqrt{x+y+1}}{x-1} \), halle: a. \( \mathrm{f}(0,1)= \) b. \( \mathrm{f}(1,0)= \) c. \( \mathrm{f}(0,0)= \) d. \( \mathrm{f}(1,1)= \) e. Halle Dominio1 answer -
Determinar las ecuaciones paramétricas y simétricas de la línea que pasa por los puntos \( P(2,3,0) \) y \( Q(10,8,12) \) \[ \begin{array}{l} x=2-8 t, y=3+5 t, z=12 t \\ \frac{x-2}{8}=\frac{y-3}{5}1 answer -
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3. xy"+y=0 Answer + y = C₁ + C₂ ln x
\[ x y^{\prime \prime}+y^{\prime}=0 \] Answer \[ y=c_{1}+c_{2} \ln x \]1 answer -
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Evaluate the double integral. \[ \iint_{D}(2 x+y) d A, \quad D=\{(x, y) \mid 1 \leq y \leq 2, y-1 \leq x \leq 1\} \]1 answer -
on Conteste la preguntas abajo utilizando la gráfica de y = f(x) a continuación 5 1. f(1) = 2 2. f(3.5) = 0 5 3. Un valor máximo local de la función ocurre en x 4. El intercepto en y ocurre en el
Conteste la preguntas abajo utilizando la gráfica de \( y=f(x) \) a continuación 1. \( f(1)= \) 2. \( f(3.5)= \) 3. Un valor máximo local de la función ocurre en \( x= \) 4. El intercepto en \( y1 answer -
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Considere la gráfica de la función y = f(x) a continuación 2 0 -2- 4 2 2) (f* g)(3) = 3) (gof)(3) = Sea g(x)=√10 x. Evalue las siguientes funciones. *Escriba las respuestas a dos lugares decimale
Considere la gráfica de la función \( y=f(x) \) a continuación Sea \( g(x)=\sqrt{10-x} \). Evalue las siguientes funciones. 'Escriba las respuestas a dos lugares decimales. * * Si está indefinido1 answer -
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I. Evalúe el integral \[ \int_{0}^{4} \int_{0}^{\pi / 2} \int_{0}^{1-x} x \cos y d z d y d x \] II.Calcule el volumen del sólido en la figura dada. III. Reescriba el integral utilizando el orden dxd1 answer -
1) Determine masa y el centro de masa del sólido con densidad dada acotado por las gráficas de las ecuaciones. Establezca y evalúe claramente el integral triple que permite determinarlo. \( x=0, x=1 answer -
Describe the domain of the function \( f(x, y)=\ln (4-x-y) \). \[ \begin{array}{l} \{(x, y): y \leq x-4\} \\ \{(x, y): x \geq 0, y \geq 0\} \\ \{(x, y): y1 answer -
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can you solve question 20 for me
Finding Local Extrema Find all the local maxima, local minima, and saddle points of the functions in Exercises 1-30. 1. \( f(x, y)=x^{2}+x y+y^{2}+3 x-3 y+4 \) 2. \( f(x, y)=2 x y-5 x^{2}-2 y^{2}+4 x+1 answer -
\( \begin{array}{l}\sigma=\sin 2 x \cos 2 y \\ \qquad T=\left\{(x, y, z): 0 \leq x \leq \frac{\pi}{4}, \quad \frac{\pi}{4}-x \leq y \leq \frac{\pi}{4}, \quad 0 \leq z \leq 6\right\} \\ \sigma=x^{2} y^0 answers -
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Una función f está definida para todo x real por . Sin calcular esta integral, halle un polinomio cuadrático tal que
\( P(x)=a x^{2}+b x+c \) \( f(x)=3+\int_{0}^{x} \frac{1+\operatorname{sen}(t)}{2+t^{2}} d t \) \( P(0)=f(0), \quad P^{\prime}(0)=f^{\prime}(0) \) y \( P^{\prime \prime}(0)=f^{\prime \prime}(0) \)1 answer -
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(1 point) Evaluate the double integral \( \iint_{R} 2 \sin (7 x-y) d A= \) where \( R=\{(x, y) \mid 0 \leq x \leq \pi / 2,0 \leq y \leq \pi / 2\} \)1 answer -
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\( 1.1 \quad \frac{d y}{d x}-\frac{y}{x}=e^{\frac{y}{x}} \) [Hint: Put \( \left.y=v x\right] \) \( 1.2 \frac{d y}{d x}-2 y \tan x=y^{2} \tan ^{2} x \)1 answer -
Let \( f(x, y, z)=\frac{\tan ^{-1}\left(x+y-z^{6}\right) \ln \left(y+z^{2}-\cos (x y z)\right)}{\sqrt{\cos (x-y) \sin (x+y z)-\pi}} \). pute \( \operatorname{div}(\operatorname{curl} \nabla f) \).1 answer -
Find the gradient vector field of f f (x, y) = ln(x − 2y)
Find the gradient vector field of \( f \), \[ f(x, y)=\ln (x+2 y) \] A. \( \nabla f(x, y)=\frac{1}{x+2 y} \hat{i}-\frac{2}{x+2 y} \hat{j} \) B. \( \nabla f(x, y)=\frac{1}{2 y} \hat{i}+\frac{2}{x+2 y}1 answer -
Find the divergence of the vector field, \[ \vec{F}(x, y, z)=e^{x} \sin y \hat{i}+e^{y} \sin z \hat{j}+e^{z} \sin x \hat{k} \] A. \( \nabla \cdot \vec{F}=e^{z} \sin y+e^{x} \sin z+e^{y} \sin x \) B. \1 answer -
37. a) Evaluate \( \iint_{R} \sin \left(\sqrt{x^{2}+y^{2}}\right) d A \), where \( R=\left\{(x, y): x \geq 0, y \geq 0,1 \leq x^{2}+y^{2} \leq 2\right\} \) b) Evaluate \( \iint_{R} \frac{y^{2}}{x^{2}+1 answer -
(Valor 1.25) Un cuerpo se desplaza por el espacio siguiendo la \( \boldsymbol{r}(t)= \) \( \left(t+t^{2}\right) \hat{\imath}+\frac{t^{2}+2}{\sqrt{2}} \hat{\jmath}+\frac{4 t^{3}-t}{3} \widehat{\boldsym1 answer -
(Valor 1.25) se logró determinar bajo análisis que la ecuación posición de un cuerpo es \( r(t)=t \hat{\imath}+\frac{2}{3} t^{\frac{3}{2}} \widehat{\boldsymbol{k}} \), determine el cambio de la ve1 answer -
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Let \( f(x, y, z)=\frac{\tan ^{-1}\left(x+y-z^{6}\right) \ln \left(y+z^{2}-\cos (x y z)\right)}{\sqrt{\cos (x-y) \sin (x+y z)-\pi}} \). Compute \( \operatorname{div}(\operatorname{curl} \nabla f) \).1 answer -
Find the following inverse Laplace transforms
Hallar las siguientes transformadas de Laplace inversas: 1. \( L^{-1}\left\{\frac{1}{s^{4}}\right\} \) 2. \( L^{-1}\left\{\frac{1}{s^{2}}-\frac{48}{s^{5}}\right\} \) 3. \( L^{-1}\left\{\frac{1}{4 s+1}1 answer -
Discuss how you determine the Laplace transform of the following function:
Problema: Discuta como usted determina la transformada de Laplace de la siguiente función: \[ f(t)=\left\{\begin{array}{c} 2,0 \leq t1 answer -
2. Convierta la ecuación r = 3sece a coordenadas rectángulares x² + y² - 3y = 0 x² + (y - 3)² = 0 x² + y² - 3x = 0 y = 3 x=3
2. Convierta la ecuación \( r=3 \sec \theta \) a coordenadas rectángulares \[ \begin{array}{l} x^{2}+y^{2}-3 y=0 \\ x^{2}+(y-3)^{2}=0 \\ x^{2}+y^{2}-3 x=0 \\ y=3 \\ x=3 \end{array} \]1 answer -
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Differentiate
1. \( f(x)=3 \sin x-2 \cos x \) 3. \( y=x^{2}+\cot x \) 7. \( y=\sec \theta \tan \theta \) 9. \( f(\theta)=(\theta-\cos \theta) \sin \theta \) 11. \( H(t)=\cos ^{2} t \)1 answer -
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Evaluate the double integral. \[ \iint_{D} \frac{y}{x^{2}+1} d A, \quad D=\{(x, y) \mid 0 \leq x \leq 9,0 \leq y \leq \sqrt{x}\} \]1 answer -
Determine whether the series converges or diverges.
\( \sum_{k=1}^{\infty} \frac{(2 k-1)\left(k^{2}-1\right)}{(k+1)\left(k^{2}+4\right)^{2}} \)1 answer -
(1 point) Find y as a function of x if y(0) = 16, y (0) = 8, y" (0) = 4, y" (0) = 0. y(x) =____ (4) - 4y + 4y = 0, 20
(1 point) Find \( y \) as a function of \( x \) if \[ y^{(4)}-4 y^{\prime \prime \prime}+4 y^{\prime \prime}=0 \] \[ \begin{array}{l} y(0)=16, \quad y^{\prime}(0)=8, \quad y^{\prime \prime}(0)=4, \qua2 answers -
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 \( z=0, x=0, z=y-5 x \) and \( y=20 \). 1. \( \int_{a1 answer -
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(1 point) Find \( d y / d x \) in terms of \( x \) and \( y \) if \( \cos ^{2}(4 y)+\sin ^{2}(4 y)=y+4 \) \( \frac{d y}{d x}= \)1 answer -
(1 point) Find \( y^{\prime} \) by implicit differentiation. Match the equations defining \( y \) implicitly with the letters labeling the expressions for \( y^{\prime} \). 1. \( 7 x \cos y+7 \sin 2 y1 answer -
Explica paso a paso que se hizo (más que nada las últimas tres líneas )
\( \begin{array}{l}\text { Ejemplo: (2) } \\ \begin{array}{l}\int e^{a x} \operatorname{sen}(b x) d x=\frac{e^{a x} \cos (b x)}{b}+\frac{a}{b} \int e^{a x} \cos (b x) d x=-\frac{e^{a x} \cos (b x)}{b}1 answer -
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Given the following functions: \[ \begin{aligned} f(x, y) & =x^{2}+y^{3}-\sin (x+y)+\ln \left(x^{2} y\right) \\ h(x, y, z) & =e^{x+y-z}+\sin \left(x z^{2}\right)+x^{3}-\frac{y}{z} \end{aligned} \] com1 answer -
8. Make a substitution to solve the following DEs. (a) \( y^{\prime}=\frac{3 y^{2}-x^{2}}{2 x y} \), let \( u=\frac{y}{x} \). (b) \( y^{\prime}+1=(y+x)^{2} \), let \( u=x+y \). (c) \( 2 y y^{\prime}=\1 answer -
intercept xy² = 5 relative minimum relative maximum point of inflection (x, y) = (x, y) = (x, y) (x, y) K
\[ x y^{2}=5 \] intercept \[ (x, y)=(\quad) \] relative minimum \( \quad(x, y)= \) relative maximum \( \quad(x, y)= \) point of inflection \[ (x, y)=(\quad) \]1 answer -
1. Find y' given the following equations. (a) y = (x²+x-4)³ Product Rule (b) y = x² sin (7x) (c) y = ln (x ln x) (d) y = log5 (1 + 2x) sd (e) y = ln (sec 5x + tan 5x) omlov on Chain (f) y = sin-¹
1. Find \( y^{\prime} \) given the following equations. (a) \( y=\left(x^{2}+x^{-4}\right)^{3} \) (b) \( y=x^{2} \sin (\pi x) \) (c) \( y=\ln (x \ln x) \) (d) \( y=\log _{5}(1+2 x) \) (e) \( y=\ln (\s1 answer