Advanced Math Archive: Questions from January 11, 2023
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scalar field \[ \phi(x, y, z)=\cos (-x) \cdot e^{y}+10 \] Show/hide Calculate the gradient of \( \phi \). \[ \nabla \phi= \]2 answers -
2 answers
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Para cacular gra- dientes de funciones, jacobianos, inversas de matrices, etc. puede utilizar biblio- tecas preestablecidas en python, en estos problemas el inter ́es es en aplicar los algoritmos cor
1. Considere el siguiente problema \[ \begin{array}{ll} \text { Minimize } & \lambda^{2}+2 \lambda \\ \text { subject to } & -3 \leq \lambda \leq 6 \end{array} \] Construya 6 iteraciones del método d0 answers -
ASAP
3. For what value(s) of \( \mathbf{h} \) will \( \mathbf{y} \) Span \( \left\{v_{1}, v_{2}, v_{3}\right\} \) if \[ v_{1}=\left[\begin{array}{l} 1 \\ 0 \\ 1 \end{array}\right] \quad v_{2}=\left[\begin{2 answers -
a) Find a potential function U for F b) Write the integral as an ordinary integral, where C is the boundary of the rectangular region [-1,1] x [-2, 2] in the z=1 counterclockwise plane. c) Use the i
\( \mathbf{F}(x, y, z)=\left(2 x e^{x^{2}+y^{2}+z^{2}}+\operatorname{sen}(z)+y\right) \mathbf{i}+\left(2 y e^{x^{2}+y^{2}+z^{2}}+x\right) \mathbf{j}+\left(2 z e^{x^{2}+y^{2}+z^{2}}+x \cos (z)\right) \2 answers -
Let D be the region in the first quadrant bounded by the curves . Consider the double integral a) Make a sketch of region D. b) Write the double integral in terms of repeated in
\( \iint_{\mathscr{D}} \frac{x y}{\left(\sqrt{x^{2}+y^{2}}\right)^{3}} d A \) Sea \( \mathscr{D} \) la región en el primer cuadrante limitada por las curvas \( x^{2}+y^{2}=1, x^{2} / 4+y^{2}=1 \). C1 answer -
a) Calculate the curl of F. b) Determine a potential function U For The Vector Field F. c) By setting up the line integral of F along the path r(t)=<cos(t),sin(t),t> from P(0,1,) hasta Q(-1,0,)
\( \mathbf{F}(x, y, z)=\left(e^{x} \operatorname{sen}(z)+2 y z\right) \mathbf{i}+(2 x z+2 y) \mathbf{j}+\left(e^{x} \cos (z)+2 x y\right) \mathbf{k} \) \[ \mathbf{F}(x, y, z)=\left(e^{x} \opera2 answers