Calculus Archive: Questions from June 05, 2023
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Utilizando la ecuación \[ A^{-1}=\frac{1}{\operatorname{det}(A)}(\operatorname{adj} A) \] Encuentre la matriz inversa de la matriz principal del siguiente sistema de ecuaciones: \[ \begin{array}{l} x2 answers -
Halle la masa y centro de masa de la lámina que ocupa la región \( D \) y que tiene la función de densidad \( \rho \) dada. \( D \) es la región triangular con vértices \( (0,0),(2,1),(0,3) ; \rh2 answers -
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Evaluate \( \iiint_{W} f(x, y, z) d V \) for the function \( f \) and region \( \mathcal{W} \) specified: \[ f(x, y, z)=42(x+y) \quad \mathcal{W}: y \leq z \leq x, 0 \leq y \leq x, 0 \leq x \leq 1 \]2 answers -
Let \( F(x, y, z)=\left(y e^{x}+e^{z}\right) \mathbf{i}+e^{x} \mathbf{j}+x e^{z} \mathbf{k} \) be a vector field. (a) Find \( \operatorname{curl}(\mathbf{F}) \) and \( \operatorname{div}(\mathbf{F})2 answers -
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Which one of the following equals \[ \int_{-1}^{0} \int_{x}^{-x}(x+y) d y d x \text {. } \] A. \( \int_{3 \pi / 4}^{5 \pi / 4} \int_{0}^{-1} r^{2}(\cos \theta+\sin \theta) d r d \theta \) B. \( \int_{2 answers -
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Solve: dy/dx= secy/y^2(x^2-3x^2+x-3)
Solve: \[ \frac{d y}{d x}=\frac{\sec y}{y^{2}\left(x^{2}-3 x^{2}+x-3\right)} \]2 answers -
Which one of the following equals \[ \int_{-1}^{0} \int_{x}^{-x}(x+y) d y d x \] A. \( \int_{3 \pi / 4}^{5 \pi / 4} \int_{0}^{1} r(\cos \theta+\sin \theta) d r d \theta \) B. \( \int_{3 \pi / 4}^{5 \p2 answers -
6.10C
Evaluate the triple integral. \[ \iiint_{E} y d V, \text { where } E=\{(x, y, z) \mid 0 \leq x \leq 3,0 \leq y \leq x, x-y \leq z \leq x+y\} \]2 answers -
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Question 6. Solve using Laplace transform x' (t) = x - y, y' (t) = 2x + 4y, x(0) = -1, y(0) = 0
Question 6. Solve using Laplace transform \[ \begin{array}{ll} x^{\prime}(t)=x-y, & x(0)=-1, \\ y^{\prime}(t)=2 x+4 y, & y(0)=0 \end{array} \]2 answers -
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1.- Resuelva cada una de las siguientes ecuaciones diferenciales. a) \( y^{\prime \prime}+4 y^{\prime}+4 y=0 \) b) \( y^{\prime \prime}+4 y^{\prime}+4 y=e^{-2 x} \)2 answers -
Use separation of variables to solve the initial value problem. 70) \( y^{\prime}=\frac{x \cos x}{y^{2}} \) and \( y=9 \) when \( x=\pi \) A) \( y=\sqrt[3]{\frac{1}{3}} \sqrt[3]{x \sin x+\cos x+2188}2 answers -
\( g(x, y)=\sqrt{\frac{1}{4}-x^{2}-y^{2}}, f(x, y)=\frac{y^{2}-x y}{y^{2}-x^{2}} \) Find \( \lim _{(x, y) \longrightarrow(1,2)} f(x, y) \) and show that \( \lim _{(x, y) \longrightarrow(0,0)} f(x, y)2 answers -
Evalúe la integral de superficie. \( \iint_{S} x z d S \), es la parte del plano \( 2 x+2 y+z=4 \) que está en el primer octante 6 5 3 42 answers -
compruebe que las funciones dadas forman un conjunto fundamental de soluciones de la ecuación diferencial en el intervalo que se indica. Forme la solución general. 27. \( x^{2} y^{\prime \prime}-6 x2 answers -
10) \( \int\left(3 x^{8}-7 x^{3}+6\right) d x \) A) \( 9 x^{9}-\frac{7}{3} x^{4}+6 x+C \) B) \( 9 x^{9}-\frac{7}{4} x^{4}+6 x+C \) C) \( \frac{1}{3} x^{9}-\frac{7}{4} x^{4}+6 x+C \) D \( \frac{1}{3} x2 answers -
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\[ f_{(x, y)}=x^{3}+3 x^{2} y^{2}-2 y^{3}-x+y \] Find the partials: a) \( f_{x}(x, y) \) and b) \( f_{y}(x, y) \).2 answers -
\[ f_{(x, y)}=x^{3}+3 x^{2} y^{2}-2 y^{3}-x+y \] Find the partials: a) \( f_{x}(x, y) \) and b) \( f_{y}(x, y) \).2 answers -
10.Find \( \frac{d y}{d x} \) for each of the following: a. \( y=\ln \left(e^{x}-2\right) \) b. \( y=\ln \left(x^{4}(x+6)^{3}\right. \) c. \( y=\frac{e^{3 x}}{x^{6}} \)2 answers -
Find the result of the following sums
6. Halle el resultado de las siguientes sumas. (a) \( \sum_{i=1}^{6} \frac{j+1}{j+3} \) (b) \( \sum_{i=2}^{5}\left(j^{2}+j\right) \)2 answers -
5) Find the derivative for: a) \( y=\sin ^{3} x \) b) \( y=\left(3 x^{2}+7 x\right)^{10} \) c) \( f(x)=\sqrt{1+\tan x} \) d) \( y=x^{2} \cos x \) e) \( y=\ln \left(x^{4}+1\right) \) f) \( y=\log _{3}2 answers -
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\[ \begin{array}{l} \mathbf{A}=\left[\begin{array}{ll} 6 & -7 \\ 1 & -1 \end{array}\right] \\ \mathbf{B}=\left[\begin{array}{ll} 7 & -8 \\ 1 & -1 \end{array}\right] \\ \mathbf{C}=\left[\begin{array}{r2 answers -
21. \( \mathrm{Si}: \) \[ \begin{array}{l} \mathbf{A}=\left[\begin{array}{rr} 7 & -4 \\ 2 & -1 \end{array}\right] \\ \mathbf{B}=\left[\begin{array}{rr} 3 & 1 \\ 2 & -4 \end{array}\right] \\ \mathbf{C}2 answers -
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Simplify. \[ \frac{\frac{x}{y}-\frac{y}{x}}{\frac{1}{y}+\frac{1}{x}} \] \[ \frac{\frac{x}{y}-\frac{y}{x}}{\frac{1}{y}+\frac{1}{x}}= \]2 answers -
Consider the following. \[ \sin \left((9.85)^{2}+(8.15)^{2}\right)-\sin \left(9^{2}+9^{2}\right) \] Find \( z=f(x, y) \) \[ f(x, y)= \]2 answers -
For the function, find the partials \( f_{x}(x, y) \) and \( f_{y}(x, y) \). \[ f(x, y)=(x+y)^{-3} \] (a) \( f_{x}(x, y) \) (b) \( f_{y}(x, y) \)2 answers -
Find \( \iint_{D}(4 x+3 y) d A \) where \( D=\left\{(x, y) \mid x^{2}+y^{2} \leq 4, x \geq 0\right\} \)2 answers -
En los problemas 43 a 48 cada figura representa la gráfica de una solución particular de una de las siguientes ecuaciones diferenciales. \[ y^{\prime \prime}+2 y^{\prime}+y=0 \] Relacione una curva2 answers -
resuelva la ecuación diferencial dada usando coeficientes indeterminados. 10. \( y^{\prime \prime}+2 y^{\prime}=2 x+5-e^{-2 x} \)2 answers -
resuelva el problema con valores iniciales. \( 68 y^{\prime \prime}+5 y^{\prime}-6 y=10 e^{2 x}, \quad y(0)=1, y^{\prime}(0)=1 \)2 answers -
Evaluate the double integral. \[ \iint_{D} 3 y^{2} e^{x y} d A, D=\{(x, y) \mid 0 \leq y \leq 8,0 \leq x \leq y\} \]2 answers -
calculate the integral of the following exercise
Curva \( y=x^{2}-7 x+6 \), el eje \( x \) y por las rectas \( x=2 \) y \( x=6 \)1 answer