Advanced Math Archive: Questions from November 19, 2022
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(40 points) Solve the initial value problem \[ y^{\prime \prime}+1 x y^{\prime}-4 y=0, y(0)=3, y^{\prime}(0)=0 \] \[ y= \]2 answers -
67 , 69
67-70 Describe the level surfaces of the function. 67. \( f(x, y, z)=2 y-z+1 \) 68. \( q(x, y, z)=x+y^{2}-z^{2} \) 69. \( q(x, y, z)=x^{2}+y^{2}-z^{2} \) 70. \( f(x, y, z)=x^{2}+2 y^{2}+3 z^{2} \)2 answers -
Considering the initi y′′−2y′+10y=e0.5x,y(0)=1,y′(0)=0.5. complete the table using Euler's method xy(x) 0 1 0.3 0.6 0.9 1.2 al value problem
(1 point) Cosiderando el problema de vaiores iniclales. \[ y^{\prime \prime}-2 y^{\prime}+10 y=e^{a .5 x}, \quad y(0)=1, \quad y^{\prime}(0)=0.5 \] completa la tabla usando el método de Euler2 answers -
Considering the initial value problem dydx=x+y5+4e−y,y(3)=−2 Complete the table with the values obtained by the Runge-Kutta method of order 2 using a2=0.9 and h=0.3. x y with Runge-Kutta or
(1 point) Considerando el problema de valores iniciales \[ \frac{d y}{d x}=\frac{x+y}{5}+4 e^{y}, \quad y(3)=-2 \] completa la tabla con los valores obtenidos por el metodo de Runge-Kutta de orden 2 u0 answers -
Tell which of the following matrices can be reduced to one diagonal and find a change-of-basis (real) matrix: (a) \( \left(\begin{array}{rrr}-1 & -3 & 1 \\ -3 & 5 & -1 \\ -3 & 3 & 1\end{array}\right)1 answer -
Calcular \( A^{50} \) donde \[ A=\left(\begin{array}{ccc} 1 & 2 & -2 \\ 2 & 1 & -2 \\ 2 & 2 & -3 \end{array}\right) \]2 answers -
E.7 Determinar los coeficientes \( a, b, c, d, e \) y \( f \) de la matriz \[ A=\left(\begin{array}{lll} 1 & 1 & 1 \\ a & b & c \\ d & e & f \end{array}\right) \] sabiendo que \( (1,1,1),(1,0,-1) \) y2 answers -
E.8 Determinar para qué valores \( a, b \in \mathbb{R} \), la matriz \[ A=\left(\begin{array}{rrr} a & b & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1 \end{array}\right) \in \mathcal{M}_{3}(\mathbb{R}) \] es diagon2 answers -
Dada la matriz \[ A=\left(\begin{array}{ccc} 2 & -2 & 6 \\ 0 & a & 4-a \\ 0 & a & -a \end{array}\right) \] probar que ésta es diagonalizable para todo \( a \neq 0 \).2 answers -
Hallar la potencia \( n \)-ésima de la matriz \[ A=\left(\begin{array}{lll} a & b & b \\ b & a & b \\ b & b & a \end{array}\right) \]2 answers -
(40 points) Solve the initial value problem \[ y^{\prime \prime}+4 x y^{\prime}-16 y=0, y(0)=1, y^{\prime}(0)=0 \] \[ y= \]2 answers -
(40 points) Solve the initial value problem \[ y^{\prime \prime}+4 x y^{\prime}-16 y=0, y(0)=1, y^{\prime}(0)=0 \] \[ y= \]2 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 \( z=0, x=0, z=y-2 x \) and \( y=4 \). \[ \begin{arra2 answers -
2 answers
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2 answers
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What is a region in the plane xy for which the diferential equation x(dy/dx)=y has a unique solution that passes through the point (x0,y0)?
2. Una región en el plano- \( x y \) para la cual la ecuación diferencial \( x \frac{d y}{d x}=y \) tiene solución única que pasa por el punto \( \left(x_{0}, y_{0}\right) \) es: a) Todo \( \left(2 answers -
What is an integrating factor of the linear diferential equation shown below:
3. Un factor integrante de la ecuación diferencial lineal \( x^{2} y^{\prime}+x(x+2) y=e^{x} \) es: a) \( x^{2} \) b) \( e^{x} \) c) \( x^{2} e^{x} \) d) \( e^{\frac{x^{3}}{3}+\frac{x^{2}}{2}} \) e)2 answers -
Solve: \[ \begin{array}{l} y^{\prime \prime \prime}+4 y^{\prime \prime}-y^{\prime}-4 y=0 \\ y(0)=0, y^{\prime}(0)=-1, y^{\prime \prime}(0)=-15 \\ y(t)= \end{array} \]2 answers -
Problemas de asignación: 1. Suma, resta las siguientes matrices a. \( \left[\begin{array}{ccc}-3 & 5 & 4 \\ 2 & -1 & 7\end{array}\right]+\left[\begin{array}{ccc}6 & 2 & -3 \\ 4 & 1 & 10\end{array}\ri2 answers -
2 answers
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number 12 please
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+2 answers -
number 14 please
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+2 answers -
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