Advanced Math Archive: Questions from June 13, 2023
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\( \begin{array}{l}f(x, y, z)=x^{2} y+y^{2} z+z^{2} x \text { ve } g(x, y, z)=x^{2} z+y^{2} x+z^{2} y \\ (\nabla f \times \nabla g){ }_{(\nabla, 0,1)}=?\end{array} \)2 answers -
\( \begin{array}{l}\text { ve: } \frac{\partial^{2} u}{\partial x \partial y}=\frac{\partial u}{\partial y} \\ u=h(x) e^{y}+f(y) \\ u=h(y) e^{x}+f(x) \\ u=c e^{k y+\frac{x}{c}} \\ u=c x e^{k y+\frac{x2 answers -
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57. Hallar la ecuación del plano tangente a cada superficie \( z=f(x, y) \) en el plano indicado: a) \( z=x^{3}+y^{3}-6 x y,(1,2,-3) \) b) \( z=(\cos x)(\sin y),\left(0, \frac{\pi}{2}, 1\right) \)2 answers -
63. Una función \( f: \mathbb{R}^{n} \rightarrow \mathbb{R} \) se llama una función par si \( f(x)=f(-x) \) para todo \( x \in \mathbb{R}^{n} \). Si \( f \) es diferenciable y par, hallar \( D f \)2 answers -
69. Evaluar todas las primeras y segundas derivadas parciales de las siguientes funciones: a) \( f(x, y)=x \arctan \left(\frac{x}{y}\right) \) b) \( f(x, y)=\cos \sqrt{x^{2}+y^{2}} \) c) \( f(x, y)=e^2 answers -
75. Hallar los extremos de \( f \) sujetos a las restricciones enunciadas. a) \( f(x, y)=x-y, x^{2}+y^{2}+z^{2}=2 \) b) \( f(x, y)=x, x^{2}+2 y^{2}=3 \) c) \( f(x, y)=3 x+2 y, 2 x^{2}+3 y^{2}=3 \)0 answers -
81. Diseñar una lata cilindríca (con tapa) que contenga 1 litro de agua, usando la mínima cantidad de metal.2 answers -
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Resolver la ecuación diferencial dada por coeficientes indeterminados. y'' − 12 y' + 36 y = 18 x + 72 answers
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x^2y''+ xy'+ (x^2 − 1/16)y = 0 Ecuación de Bessel mostrarle por favor mostrar todo el trabajo? salud0 answers
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