Advanced Math Archive: Questions from August 10, 2022
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Find the solution \( u(x, y) \) of \[ \left\{\begin{array}{l} u_{x}+\sin (x) u_{y}=y \\ u(x=0, y)=0 . \end{array}\right. \]1 answer -
Ejercicio2: Usar coordenadas polares para evaluar la integral \[ \iint_{R} \sin \left(x^{2}+y^{2}\right) d A \] Donde \( \mathrm{R} \) es la región \( 11 answer -
Ejercicio5: Halle el volumen del sólido que se encuentra en el primer octante, limitado por el cilindro \( z=9-y^{2} \) y el plano \( x=2 \)1 answer -
Find a particular solution to \[ y^{\prime \prime}-2 y^{\prime}+y=\frac{15.5 e^{t}}{t^{2}+1} \] \[ y_{p}= \]1 answer -
1 answer
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6. Sketch the feasible cone \( D_{x} \) and the cone of descent \( F_{x} \) at \( (x, y)=(0,0) \), and find their intersection, in all the following cases: (a) \( f(x, y)=x+y, S=\{x \geq 0, y \geq 0\}1 answer -
Let \( A=\left(\begin{array}{ccc}3 & -1 & 0 \\ 0 & 2 & -1 \\ 3 & -4 & 2\end{array}\right), B=\left(\begin{array}{ccc}-1 & -1 & 0 \\ 2 & 3 & -5\end{array}\right) \). Find \( A B \), BA if possible.1 answer -
Exprers as summation \[ 1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\frac{1}{16}-\frac{1}{32}+\frac{1}{64 .} \]1 answer