Advanced Math Archive: Questions from March 27, 2023
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2. Solve the given IVP. \[ 2 x \sin (y) d x+\left(x^{2} \cos (y)-1\right) d y=0 \text { subject to } y(0)=\frac{1}{2} \]2 answers -
6. Find a particular solution ( 1.5 points) a. \( y^{\prime \prime}-y^{\prime}-6 y=6 x-5 \) b. \( y^{\prime \prime}-2 y^{\prime}+y=e^{x} \) c. \( y^{\prime \prime}-2 y^{\prime}+y=\sin x \)2 answers -
Problema de Optimización Lagrange 1. Objetivo determinar los puntos frontera de \( x^{2}+y^{2}=25 \) si \( T(x, y)=4 x^{2}-4 x y+y^{2} \) ¿Temperatura máxima y mínima?2 answers -
5. Find a particular solution for a. \( y^{\prime \prime}-y^{\prime}+y=\sin x \) b. \( y^{\prime \prime}-5 y^{\prime}+4 y=8 e^{x} \)2 answers -
Bxeroise 6.4 Solve the following differential equations. 1. \( x y^{\prime}-\mathrm{y}=\mathrm{x}^{3} \mathrm{y}^{4} \) 2. \( x y^{\prime}+y=x^{4} y^{3} \) 4. \( y y^{\prime}=y^{2}-1 \) 5. \( y^{\prim2 answers -
2 answers
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Find the derivatives of the following functions: (1) \( y=3 x^{2 / 3}-4 x^{\frac{1}{2}}+\sqrt{\pi} \) (2) \( y=\frac{x^{2}+3 x-e}{x} \) (3) \( y=(x-\sqrt{x})(x+\sqrt{x}) \) (4) \( y=\frac{2-x}{3 x+1}2 answers -
20,22,24,26,28, and 30 please
20. \( y^{\prime \prime}(\theta)+4 y(\theta)=\sin \theta-\cos \theta \) 21. \( y^{\prime \prime}(\theta)+2 y^{\prime}(\theta)+2 y(\theta)=e^{-\theta} \cos \theta \) 22. \( y^{\prime \prime}(x)+6 y^{\p3 answers -
\( \begin{array}{l}p=x+2 y \\ x+y \leq 25 \\ y \geq 10 \\ 2 x-y \geq 0 \\ x \geq 0, y \geq 0\end{array} \)2 answers -
2. (20 puntos) Se usa el procedimiento indicado en el diagrama de flujo con \( a=-2, b=0 \) y \( n=3 \) para encontrar una raiz de la función: \( f(x)=x^{4}-4 x^{3}+x-10 \) El valor de c que se despl0 answers -
3. Considerese el metodo de Gauss-Seidel para el sistema de ecuaciones lineales siguientes asegurando la convergencia. En la diagonal, póngase las variables en orden alfabético. \[ \begin{array}{l}2 answers -
4. (25 puntos) Usa el método de Gauss-Seidel para resolver el sistema de ecuaciones lineales siguiente: \[ \begin{array}{c} 4 x+6 y-z=9 \\ 3 y-2 x+8 z=51 \\ 10 x+y+2 z=3 \end{array} \] Complete la ta2 answers -
5. Use el método de Newton Raphson para hallar una raíz de la función: \[ 3 x-\cos \left(e^{2 x}\right)=5 \] tomando \( x_{0}=1 \), use como criterio de paro un error aproximado absoluto \( E_{|b|}2 answers -
Problem 2.4 Solve the I.V.P. \[ y^{\prime \prime}-4 y^{\prime}+13 y=5 \cos (3 x), \quad y(0)=4, \quad y^{\prime}(0)=5 \]2 answers -
3,6,9,12,15,18 show work plzz
1. \( x^{\prime}=-x+3 y, y^{\prime}=2 y \) 2. \( x^{\prime}=x-2 y, y^{\prime}=2 x-3 y \) 3. \( x^{\prime}=-3 x+2 y, y^{\prime}=-3 x+4 y ; x(0)=0, y(0)=2 \) 4. \( x^{\prime}=3 x-y, y^{\prime}=5 x-3 y ;2 answers -
\( \frac{4 x^{2}}{2 h^{2}}=\operatorname{tin}^{3} \) \( \frac{d^{2} x}{d r^{2}}=d r^{2} \) \( \frac{\partial x^{2}}{2 r^{7}}=4 x^{4} \) \( \frac{\partial^{2}}{\partial^{2}}=30 x^{2} \) \( \frac{\parti2 answers -
Find (3)BA + (4)AC, if possible. \[ A=\left[\begin{array}{rrr} 2 & 1 & -1 \\ 0 & 2 & -2 \end{array}\right] B=\left[\begin{array}{rr} -3 & 3 \\ 2 & 0 \end{array}\right] C=\left[\begin{array}{rrr} -3 &2 answers -
Find \( A C D \), if possible. \[ A=\left[\begin{array}{rrr} 2 & -1 & 1 \\ 0 & 2 & -2 \end{array}\right] \quad C=\left[\begin{array}{rrr} -2 & 0 & 1 \\ 1 & -2 & 2 \\ -2 & 1 & 1 \end{array}\right] \qua2 answers -
Let f(x,y) = exy. Compute ∂2023f (x, y).
Problem 1. Let \( f(x, y)=e^{x y} \). Compute \[ \frac{\partial^{2023} f}{\partial x^{2021} \partial y^{2}}(x, y) \]2 answers -
\( y=\sqrt[3]{x-2} \cdot \ln (3 x+1)(4 \mathrm{pts}) \) \( g(x)=e^{3 x^{2}}+\frac{2 x-1}{4+x^{2}}(4 \mathrm{pts}) \)0 answers -
(1 point) Usa el método de Gauss-Seidel para resolver el sistema de ecuaciones lineales siguientes realizando los intercambios de renglones que sean necesarios para asegurar la convergencia. \[ \begi2 answers -
Find the curl 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 \times \vec{F}=-e^{y} \cos y \hat{i}-e^{z} \cos z \hat{j}+e^{x} \c2 answers -
2 answers
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Find the gradient vector field of \( f \), \[ f(x, y, z)=x \cos \left(\frac{y}{z}\right) \] A. \( \nabla f(x, y, z)=\cos \left(\frac{y}{z}\right) \hat{i}+\frac{x}{z} \sin \left(\frac{y}{z}\right) \hat2 answers -
Rewrite the following iterated integral using five different orders of integration. \[ \begin{array}{c} \int_{-3}^{3} \int_{-\sqrt{9-x^{2}}}^{\sqrt{9-x^{2}}} \int_{x^{2}+y^{2}}^{9} g(x, y, z) d z d y2 answers -
2 . If \[ \mathbf{x}=\left(\begin{array}{c} 2 \\ 3 i \\ 1-i \end{array}\right) \text { and } \mathbf{y}=\left(\begin{array}{c} -1+i \\ 2 \\ 3-i \end{array}\right) \] find (a) \( \mathbf{x}^{T} \mathbf0 answers -
2 answers
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0 answers
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completar la tabla y gráfica
\[ \frac{x^{2}}{9}+\frac{z^{2}}{49}=1 \] Descripción: Gráfica en Geogebra2 answers -
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}2 answers -
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}2 answers -
Calculate \( \iint_{S} f(x, y, z) d S \) For \[ y=4-z^{2}, \quad 0 \leq x, z \leq 5 ; \quad f(x, y, z)=z \] \[ \iint_{S} f\left(x, y_{1} z\right) d S= \]2 answers -
24,26,28,30 please
In Problems 23-30, find the solution to the initial value problem. 23. \( y^{\prime}-y=1, \quad y(0)=0 \) 24. \( y^{\prime \prime}=6 t ; \quad y(0)=3, \quad y^{\prime}(0)=-1 \) 25. \( z^{\prime \prime3 answers -
2 answers
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(1 point) Considérese el método de Gauss-Seidel para el sistema de ecuaciones lineales siguientes realizando los intercambios de renglones que sean necesarios para asegurar la convergencia. En la di0 answers -
(1 point) Let \( x, y, z \) be (non-zero) vectors and suppose \( w=4 y-x+3 z \). If \( z=x-4 y \), then \( w= \) \[ x+ \] \( y \). Using the calculation above, mark the statements below that must be t2 answers