Calculus Archive: Questions from November 04, 2022
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Determine la función de carga en el capacitor para todo tiempo t y con ella obtenga la carga en el capacitor después de 3 segundos en un circuito LRC en serie formado por un inductor con \( L=4 H \)0 answers -
Indique cuál opeión contiene la forma de la solución general a la ED: \[ \begin{array}{c} -25 y+y^{\prime \prime}=3 x^{2}+5 \operatorname{sen}(2 x) \\ y=C x^{2}+C_{1} e^{-5 x}+C_{2} e^{5 x}+B \cos2 answers -
please solve number 8
Evaluate the triple integral. \[ \iiint_{E} y d V, \text { where } E=\{(x, y, z) \mid 0 \leq x \leq 5,0 \leq y \leq x, x-y \leq z \leq x+y\} \]2 answers -
1 point Find \( f_{1}^{\prime}(x, y), f_{2}^{\prime}(x, y), f_{12}^{\prime \prime}(x, y) \) for \( f(x, y)=x^{5} \ln y \) \[ \begin{array}{l} f_{1}^{\prime}(x, y)=5 x^{4} \ln y, f_{2}^{\prime}(x, y)=\2 answers -
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1 point Find \( f_{1}^{\prime}(x, y), f_{2}^{\prime}(x, y), f_{12}^{\prime \prime}(x, y) \) for \( f(x, y)=\left(x^{2}-2 y^{2}\right)^{5} \) \[ \begin{array}{l} f_{1}^{\prime}(x, y)=5(2 x)^{4}, f_{2}^2 answers -
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Find \( y^{\prime} \) where \( y=13 \sin ^{-1}(\cos (5 x))-\tan ^{-1}(18 x) \) Answer; \[ \begin{aligned} y^{\prime} &=-\frac{65 \sin (5 x)}{\sqrt{1-\cos ^{2}(5 x)}}-\frac{18}{1+324 x^{2}} \\ y^{\prim2 answers -
3. Find \( f_{1}^{\prime}(x, y), f_{2}^{\prime}(x, y) \), and \( f_{12}^{\prime \prime}(x, y) \) for the following: (a) \( f(x, y)=x^{7}-y^{7} \) (b) \( f(x, y)=x^{5} \ln y \) (c) \( f(x, y)=\left(x^{1 answer -
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13-22 Find and sketch the domain of the function. 13. \( f(x, y)=\sqrt{x-2}+\sqrt{y-1} \) 14. \( f(x, y)=\sqrt[4]{x-3 y} \) 15. \( f(x, y)=\ln \left(9-x^{2}-9 y^{2}\right) \) 16. \( f(x, y)=\sqrt{x^{22 answers -
Evaluate each integral. \[ \begin{array}{r} \int_{x-y}^{x+y} y d z= \\ \int_{0}^{x} \int_{x-y}^{x+y} y d z d y= \end{array} \] Now evaluate \( \iiint_{E} y d V \), where \( E=\{(x, y, z) \mid 0 \leq x2 answers -
Determina si existe el limite asignado. Usa el método de tabla de valores para determinar si el límite existe y cuánto es. 1. \( \lim _{x \rightarrow 4} \frac{1}{\sqrt{x^{2}-16}}= \) 2. \( \lim _{x2 answers -
Dos tanques cada uno con \( 50 \mathrm{~L} \) de líquido, están interconectados por tubos con líquido fluyendo del tanque \( \mathrm{A} \) al tanque \( \mathrm{B} \) a razón de \( 4 \mathrm{~L} /2 answers -
Evaluate the double integral. \[ \iint_{D} 5 y \sqrt{x^{2}-y^{2}} d A, \quad D=\{(x, y) \mid 0 \leq x \leq 3,0 \leq y \leq x\} \]2 answers -
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1. Calculate the double integral. \[ \iint_{R}\left(y+x y^{-2}\right) d A, \quad R=\{(x, y): 0 \leq x \leq 2,1 \leq y \leq 4\} \]2 answers -
1. [-/5 Points \( ] \) SCALCET9 10.1.002.MI. For the given parametric equations, find the points \( (x, y) \) corresponding to the parameter values \( t=-2,-1,0,1,2 \). \[ \begin{array}{ll} & x=\ln \l3 answers -
Halle la solución general de la ED \( y^{\prime \prime}-y^{\prime}=x^{2} \), es: a. \( y(x)=c_{1}+c_{2} e^{x}-\frac{x^{3}}{3}-x^{2}-2 x \) b. \( y(x)=c_{1}+c_{2} e^{x}+\frac{x^{3}}{3}-x^{2}-2 x \) c.2 answers -
La solución particular de la ED \( y^{\prime \prime}-4 y^{\prime}=x^{2} e^{2 x} \) es de la forma: a. \( y_{p}=x e^{2 x}\left(A x^{2}+B x+C\right) \) b. \( y_{p}=x e^{x}\left(A x^{2}+B x+C\right) \)2 answers -
La solución particular de la ED \( y^{\prime \prime}-4 y^{\prime}+4 y=\sin 2 x+e^{2 x} \) es de la forma: а. \( y_{p}=A \cos 2 x+B \sin 2 x+C x e^{2 x} \) b. \( y_{p}=A \cos 2 x+B \sin 2 x+C x^{2} e2 answers -
e la solución general de la ED \( y^{\prime \prime}+y^{\prime}-6 y=\frac{1}{2} \sin 2 x \), es: a. \( y(x)=c_{1} e^{2 x}+c_{2} e^{-3 x}-\frac{1}{104}(5 \sin 2 x+\cos 2 x) \) b. \( y(x)=c_{1} e^{2 x}+2 answers -
Find \( y^{\prime} \) where \( y=\cot \left(8 x^{2}+6\right) \sqrt{8 x^{3}+25} \) Answer: \[ \begin{array}{l} y^{\prime}=-16 x \csc ^{2}\left(8 x^{2}+6\right) \sqrt{8 x^{3}+25}+\cot \left(8 x^{2}+6\ri2 answers -
Find \( y^{\prime} \) where \( y=22 \sin ^{-1}(\cos (15 x))-\tan ^{-1}(8 x) \) Answer: \[ \begin{aligned} y^{\prime} &=\frac{-330 \sin (15 x)}{\sqrt{1-\cos ^{2}(15 x)}}-\frac{1}{1+64 x^{2}} \\ y^{\pri2 answers -
Find \( y^{\prime} \) where \( y=\cos \left(x e^{3 x}\right)-11^{\sec x} \) Answer: \[ \begin{array}{l} y^{\prime}=-\sin \left(x e^{3 x}\right)\left(e^{3 x}+3 x e^{3 x}\right)-11^{\sec x} \ln (11) \se2 answers -
Parte 4: 28 puntos Calcula los siguientes timites al infinito: 7. \( \lim _{x \rightarrow \infty} \frac{6 x^{3}-2 x+2}{x^{3}-x} \) 8. \( \lim _{x \rightarrow \infty}\left(\sqrt{x^{2}-4}+x\right) \)2 answers -
Evaluate the following sum. \[ \sum_{i=1}^{n}(7+2 i)^{2} \] (A) \( \frac{1}{2} n\left(5 n^{2}+55 n+653\right) \) (B) \( \frac{1}{2} n\left(5 n^{2}+55 n+135\right) \) (C) \( \frac{1}{3} n\left(4 n^{2}+2 answers -
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\( y^{\prime} \) for \( y=e^{-2 x} \cos x \) \( e^{-2 x}(2 \cos x-\sin x) \) \( e^{-2 x}(-2 \cos x-\sin x) \) \( 2 e^{-2 x}(\cos x+2 \sin x) \) \( \sin x \)2 answers -
solo encontrar solución particular
(5 puntos) Dada la ecuacion diferencial \( y^{(4)}-9 y^{\prime \prime}=x^{3}+\sin x+\cos 2 x+x e^{3 x} \), escriba pero no halle la solución particular.0 answers -
(8 puntos) Se sabe que un cierto material radioactivo decae a una razón proporcional a su cantidad de material presente. Un bloque de ese material tiene originalmente una masa de 100 gramos y cuando2 answers -
d. (9 puntos) Un tanque contione incialmente 100 galones de agua pura. Agua salada entra al depósito a una razón de \( 2 \mathrm{gal} / \mathrm{min} \) con una concentración de \( 1 \mathrm{lb} / \2 answers -
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solve the differential equation
\( y^{\prime \prime}+4 y=4 \sin 2 x+4 \cos 2 x, y(\pi)=y^{\prime}(\pi)=2 \)2 answers -
(9 puntos) Use el método de reducción de orden para resolver la ecuación diferencial \( x^{2} y^{\prime \prime}-2 y=x^{2} \) si \( y_{1}=x^{2} \) (Nota: para hallar la solución particular debe uti2 answers -
Find \( y: \) \[ y=(2 x-4)(2 \times 3-x 2+1) \] \( 16 \times 3-10 \times 2+30 x+2 \) \( 16 \times 3-30 \times 2+8 x+2 \) (C) \( 4 \times 3+10 \times 2-30 x+2 \) \[ 12 \times 3+30 \times 2-10 x+2 \]2 answers -
Compute the gradient vector fields of the following functions: A. \( f(x, y)=4 x^{2}+7 y^{2} \) \( \nabla f(x, y)= \) B. \( f(x, y)=x^{3} y^{2} \) \( \nabla f(x, y)= \) C. \( f(x, y)=4 x+7 y \) \( \na2 answers -
Calculate all four second-order partial derivatives of \( f(x, y)=4 x^{2} y+8 x y^{3} \). \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y)= \]2 answers -
Calculate all four second-order partial derivatives of \( f(x, y)=(3 x+2 y) e^{y} \). \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y)= \]2 answers -
Find dy/dx and simplify your answers whenever possible: 1. \( y=\sin (8 x+9) \) 2. \( y=\tan ^{2}\left(3 x^{2}\right) \) Derivatives of 3. \( y=\cot (\tan 4 x) \) trigonometric function 4. \( y=\cos 42 answers -
2. ( 20 pts.) Find the derivative of \( y \) with respect to \( x \). a) \( y=\frac{1-\cos x}{1+\cos x} \) b) \( y=\frac{2 x}{\sqrt{x+1}} \) c) \( y=\tan \frac{2}{x} \) d) \( \cos ^{2} x+\sin ^{2} y=12 answers -
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Evaluate \( \iiint_{E} 3 x z d V \) where \( E=\{(x, y, z) \mid 0 \leq x \leq 1, x \leq y \leq 2 x, 02 answers