Advanced Math Archive: Questions from November 04, 2022
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Problem 2. Compute the following: (a) \( \int_{0}^{\infty} \frac{1}{2+3 y^{5}} d y \) (b) \( \int_{0}^{\pi} \cos ^{4} \theta d \theta \), (c) \( \int_{0}^{\pi / 2} \tan \frac{1}{2} \theta d \theta \),2 answers -
Q5) Simplify the following Boolean expression using Karnaugh map: a) \( F(x, y, z)=x^{\prime} y z+x y^{\prime} z^{\prime}+x y z+x y z^{\prime} \) b) \( F(x, y, z)=x^{\prime} y^{\prime} z^{\prime}+x^{\1 answer -
Tranlate: Solve the following differential formula
Resuelva la siguiente ecuación diferencial \[ (1+x) \frac{d y}{d x}-x y=x+x^{2} \] \( y=+\frac{3}{x+1}+\frac{x^{2}}{x+1}+\frac{3 x}{x+1}-\frac{C e^{x}}{x+1} \) \( y=-\frac{3}{x+1}-\frac{x^{2}}{x+1}-\2 answers -
Tranlate: Consider the following system of Differential Equations: , Subject to Find the of the coefficients of matrix A, enter your answers in order from least to greatest and separated by a comma
Considere el siguente sistema de Ecuaciones Diferenciales: \( \left(\begin{array}{ll}2 & 3 \\ 6 & 5\end{array}\right) \), Sujeto a \( \left(\begin{array}{c}12 \\ 3\end{array}\right) \) Encuentre los d2 answers -
Considere el siguente sistema de Ecuaciones Diferenciales: \( \left(\begin{array}{ll}2 & 3 \\ 6 & 5\end{array}\right) \), Sujeto a \( \left(\begin{array}{c}12 \\ 3\end{array}\right) \) Encuentre los d2 answers -
Solve the differential equation: \( (d y / d x)+y \cot x=5 e^{\cos x} \) (hints: use the integrating factor method, \( \int \cot =\ln |\sin | \) ) \( y \sin x=-5 e^{\ln |\sin x|}+C \) \( y \sin x=-5 e2 answers -
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Considere el siguente sistema de Ecuaciones Diferenciales: \( \left(\begin{array}{ll}2 & 3 \\ 6 & 5\end{array}\right), \operatorname{sujeto}\left(\frac{12}{3}\right) \) Encuentre los de los coeficient0 answers -
Consider the following system of differential equations: FInd the______ of the coefficients of matrix A, enter your answers from smallest to largest. Find the _____ corresponding to the smallest eigen
Considere el siguente sistema de Ecuaciones Diferenciales: \( \left(\begin{array}{ll}2 & 3 \\ 6 & 5\end{array}\right) \), Sujeto a \( \left(\begin{array}{c}12 \\ 3\end{array}\right) \) Encuentre los d2 answers -
1. Solve following questions (Inverse operator method) (1) \( y^{\prime}+2 y=\sin 2 x \) (2) \( \mathrm{y}^{\prime \prime}+4 y=\sin 2 x \) (3) \( y^{\prime}+2 y=x \) (4) \( y^{\prime \prime}+3 y^{\pri1 answer -
Find the answer to the following differential equation.
Determine la respuesta de la siguiente ecuación diferencial: \[ \begin{array}{r} y^{\prime \prime}+3 y^{\prime}+2 y=x^{2} \\ y=C_{1} e^{-2 x}+C_{2} e^{-x}+\frac{x^{2}}{2}-\frac{3 x}{2}+\frac{7}{4} \\2 answers -
Considere el siguente sistema de Ecuaciones Diferenciales: \( \left(\begin{array}{cc}10 & -20 \\ 8 & -18\end{array}\right) \), Sujeto a \( \left(\begin{array}{c}12 \\ 3\end{array}\right) \) Encuentre0 answers -
1. Solve for \( \mathrm{x}: 6^{2 x}-9\left(6^{x}\right)+14=0 \). First let \( y=6^{x}, x=\log _{6}(y) \)2 answers -
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1. Solve the initial value problem \[ \mathbf{y}^{\prime}=\left[\begin{array}{ccc} -1 & 4 & 2 \\ -2 & 5 & 2 \\ 1 & -2 & 0 \end{array}\right] \mathbf{y}, \quad \mathbf{y}(0)=\left[\begin{array}{c} 7 \\2 answers -
Solve the following ODE using the power series method i) \( y^{\prime \prime}+\sin (x) y^{\prime}+\cos (x) y=0 \) ii) \( y^{\prime \prime}+\left(1-x^{2}\right) y=0 \)2 answers -
Evaluate the integral \( \iint_{R} \sin x \cos y d A \), where \( R=\left[0, \frac{\pi}{2}\right] \times\left[0, \frac{\pi}{2}\right] \) Solution \[ \begin{aligned} \iint_{R} \sin x \cos y d A &=\int_1 answer -
Solve the system of differential equations using the cramer's rule
\( \begin{array}{rlr}x^{\prime}=4 x-2 y+2 \mathscr{U}(t-1) & \text {;sujeto a las condiciones iniciales: } & x(0)=0 \\ y^{\prime}=3 x-y+2 \mathscr{U}(t-1) & y(0)=\frac{1}{2}\end{array} \)2 answers -
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4.3.10. Solve the following boundary value problems for Laplace's equation on the square \( \Omega=\{0 \leq x \leq \pi, \quad 0 \leq y \leq \pi\} \). (a) \( u(x, 0)=\sin ^{3} x, \quad u(x, \pi)=0, \qu1 answer -
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11.2.3 Find the analytic function \[ w(z)=u(x, y)+i v(x, y) \] (a) if \( u(x, y)=x^{3}-3 x y^{2} \), (b) if \( v(x, y)=e^{-y} \sin x \).2 answers -
Se desea construir un campo rectangular de futbol en Loiza. El campo tendrá un perimetro de 320 yardas. Si el largo de medir 40 yardas más que su ancho, ¿cuáles son las dimensiones de este campo d2 answers -
1) Solve the following ODE using the power series method i) \( \quad y^{\prime \prime}+\sin (x) y^{\prime}+\cos (x) y=0 \) ii) \( y^{\prime \prime}+\left(1-x^{2}\right) y=0 \)1 answer -
2) For the following ODE determine if the method of Frobenius can be used. i) \( \quad(x+2)^{2} y^{\prime \prime}+(x+2) y^{\prime}-y=0 \) ii) \( \quad 2 x(x-1) y^{\prime \prime}-(x+1) y^{\prime}+y=0 \2 answers -
Use the Laplace transform to solve the initial value problems: 1. \( y^{\prime \prime}+4 y^{\prime}+5 y=e^{-t}(\cos t+3 \sin t), y(0)=0, y^{\prime}(0)=4 \) 2. \( \quad y^{\prime \prime}+2 y^{\prime}+22 answers -
determine the value of that maximices z=x+y
Determine el valor de \( y \) que maximiza \( z=x+y \) sujeto a las siguientes restricciones: \[ \begin{array}{l} 5 x+4 y \leq 36 \\ x+2 y \leq 18 \\ x \geq 0, y \geq 0 \end{array} \]2 answers -
Escribir las matrices de las siguientes aplicaciones lineales respecto de las s canónicas de los espacios correspondientes: Tema 5 - Aplicaciones lineales (a) \( f\left(x_{1}, x_{2}, x_{3}\right)=\le2 answers -
Use the reduction method to solve the differential equation given. Use the parameter variation method to obtain the particular solution.
(e) (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 debe2 answers -
E.3 Dar una base para \( \mathcal{M}_{3 \times 2}(\mathbb{R}) \) y hallar la matriz asociada a la aplicación lineal \( T \) (aplicación traza) definida como \( T: \mathcal{M}_{3 \times 2}(\mathbb{R}0 answers -
E.4 Sea \( T: \mathbb{P}_{\mathbb{R}}^{3}[x] \rightarrow \mathbb{P}_{\mathbb{R}}^{3}[x] \) lineal tal que \( T(1)=x^{2}+1, T(x)=-x, T\left(x^{2}\right)=x^{3} \) y \( T\left(x^{3}\right)=x^{2}+\mid x-12 answers -
Solve the differential equation given
(b) \( (8 \) puntos \( ) y^{\prime \prime \prime}-y=x^{2} \sin x \)2 answers -
Solve the differential equation given and evaluate it on the given coordenates.
(c) \( (9 \) puntos \( ) y^{\prime \prime}+4 y=4 \sin 2 x+4 \cos 2 x, y(\pi)=y^{\prime}(\pi)=2 \)2 answers -
E.6 Demostrar que las aplicaciones \( f: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2} \) dada por \( f(x, y)= \) \( (x+y, x+2 y) \) y \( g: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2} \) dada por \( g(x, y2 answers -
2. Suppose that \( g \in C^{1}(a, b) \). Show that \( |g(x)-g(y)| \leq \gamma|x-y| \) for all \( x, y \in(a, b) \quad \) if and only if \( \quad\left|g^{\prime}(x)\right| \leq \gamma \) for all \( x \2 answers -
Answer
Solve the equation or IVP. 1) \( y^{\prime \prime}+4 y^{\prime}+3 y=e^{x}, \quad y(1)=1, \quad y^{\prime}(1)=2 \) 2) \( y^{\prime \prime}-4 y=32 x, \quad y(0)=0, \quad y^{\prime}(0)=6 \) Method of Un2 answers -
PLEASE SOLVE IT
b) [08 pts] Determine the point(s) where the following function is defined \[ g(x, y)=\sqrt{-(x-6)^{4} \ln ^{4}(y+3)-9 x^{2}-36 x y-36 y^{2}} \]2 answers -
Answer
3) \( y^{\prime \prime}+2 y^{\prime}+2 y=(\cosh x)(\sin x) \quad \) Note: \( \cosh x=\frac{e^{x}+e^{-x}}{2} \) 4) \( y^{\prime \prime}-8 y^{\prime}+4 y=\cos (3 x) \) Method of Undetermined Coefficien2 answers