Advanced Math Archive: Questions from August 29, 2022
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3. Let \( f: \mathbb{R}^{2} \rightarrow \mathbb{R} \) be the function defined by \[ f(x, y)=\frac{e^{y}+e^{-x}}{\sin y} \] (a) Compute \( f_{x}(x, y) \) ( 6 marks) (b) Compute \( f_{y}(x, y) \) (7 mar1 answer -
1. Resuelva por mínimos cuadrados el sistema: \[ \left[\begin{array}{ll} 1 & 1 \\ 1 & 2 \\ 1 & 3 \\ 1 & 4 \\ 1 & 5 \\ 1 & 6 \end{array}\right] \mathbf{x}=\left[\begin{array}{r} 0.2 \\ 0.25 \\ 0.2 \\1 answer -
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clasify the next vectors from this matrix
\[ A=\left[\begin{array}{rrrr} -14 & -1 & -5 & -2 \\ -42 & 0 & -15 & -9 \\ 64 & -1 & 22 & 13 \\ -42 & 3 & -15 & -12 \end{array}\right] \] clasifique los vectores: a) \( v_{1}=\left[\begin{array}{r}1 \1 answer -
3. Use the chain rule to find \( d y / d x \) for the following: (a) \( y=\left(3 x^{2}-13\right)^{3} \) (b) \( y=\left(7 x^{3}-5\right)^{9} \) (c) \( y=(a x+b)^{5} \)1 answer -
14. Find all functions \( y=y(x) \) such that \( L[y]=\frac{6 e^{3 x}}{x} \) (a) \( y=\frac{2 e^{3 x}+C}{x} \) (b) \( y=\frac{2 e^{3 x}}{x}+C \) (c) \( y=2 x e^{3 x}+C x \) (d) \( y=2 e^{3 x}+C \) (e)3 answers -
1. Solve the following initial value problems: (a) \( y^{\prime}-\frac{x^{2}}{(y-1)^{2}}=0, \quad y(0)=4 \) (b) \( y^{\prime \prime}+7 y^{\prime}+12 y=4 \sin (3 t), \quad y(0)=\frac{-14}{75}, \quad y^1 answer -
Traverse the index in the power series so that the power of x in the summation is m.
\( \sum_{s=2}^{\infty} \frac{s(s+1)}{s^{2}+1} x^{s-1}=\sum_{m=\#}^{\infty} C(m) x^{m} \)1 answer -
Determine the singular points of one of the following differential equations and classify them. I just need to solve one of the three
Determine los puntos singulares de una de las ecuaciones diferenciales siguientes y clasifíquelos. \begin{tabular}{|c|c|c|} \hline\( x^{3} y^{\prime \prime}+4 x^{2} y^{\prime}+3 y=0 \) & \( x(x+3)^{22 answers -
Respecto al conjunto de vectores: {v1=[x54],v2=[2y2],v3=[62z]} indique en orden los valores de x, y y z para que el conjunto sea ortogonal.
Respecto al conjunto de vectores: \[ \left\{\mathbf{v}_{1}=\left[\begin{array}{l} x \\ 5 \\ 4 \end{array}\right], \mathbf{v}_{2}=\left[\begin{array}{l} 2 \\ y \\ 2 \end{array}\right], \mathbf{v}_{3}=\1 answer -
Determine projection of the vector b = [ 2 0 2 ] on the space generated by the vectors:
Determine proyección del vector \( \mathbf{b}=\left[\begin{array}{l}2 \\ 0 \\ 2\end{array}\right] \) sobre el espacio que generan los vectores: \[ \left\{\mathbf{v}_{1}=\left[\begin{array}{l} 5 \\ 32 answers -
PLS HELP. MATH 2065 Differential Equations
Solve the first order ODE's: 6. \( 2 t y^{\prime}+y=e^{t} \) 7. \( y^{\prime}+2 y=\sin t \) 8. \( t(t+1) y^{\prime}=2+y \) 9. \( y^{\prime}+y \cos t=\cos t, y(0)=0 \). 10. \( \quad y^{\prime}-\frac{2}1 answer -
Sea la ecuación de una superficie . Se puede afirmar:
(A) \( z \leq 4 \) (B) \( -4 \leq z \leq 4 \) (C) \( z \geq 4 \) (D) \( 0 \leq z \leq 4 \)1 answer