Advanced Math Archive: Questions from January 16, 2023
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\[ f(x, y)=\left\{\begin{array}{ll} x y \frac{x^{2}-y^{2}}{x^{2}+y^{2}} & , \text { if }(x, y) \neq 0 \\ 0, & \text { if }(x, y)=0 \end{array}\right. \] Calculate \( \frac{\partial f}{\partial x}(0, y2 answers -
\( 4 x y^{\prime \prime}+(2-x) y^{\prime}-y=0 \) Answer: \( \begin{aligned} r_{1} & =\frac{1}{3}, \quad r_{2}=0 \\ y & =c_{1} x^{\frac{1}{3}}\left(1+\frac{1}{3} x+\frac{1}{3^{2} \cdot 2} x^{2}+\frac{12 answers -
The integral value of f(x, y, z) =(y+z, x,x) over c=r(t) =8t-1, 2t -1-, 3t-1) where t E 1= (0 ,1) C R is:
7. 14 puntos La integral de \( f(\rho, \theta, \varphi)=\rho^{3} \) sobre la región \( E \) en \( \mathbb{R}^{3} \) que está encima del cono \( z=\sqrt{x^{2}+y^{2}} \) y debajo de la esfera \( x^{2}2 answers -
2.-) the ellipse C in R^2 centered at the origin, which intercepts the x-axis at point A =(2, 0) and the y-axis at point B= (0,3) is parameterized by the function
1. Un plano paralelo al plano \( \mathcal{P}_{1}: 2 x-\frac{1}{6} y-z=12 \) y que pasa por el punto \( (1,-12,-1) \) es: (a) \( \mathcal{P}_{2}: 12 x-y-6 z=36 \) (c) \( \mathcal{P}_{2}:-2 x \mp 6 y+z=2 answers -
\( y>1, \quad f(x, y)=\ln \left(x^{2}+y^{2}+1\right) \) (9) \( \frac{\partial f(x, y)}{\partial(y)}= \) ? (b) Using Liebnitz formula \( F^{\prime}(y)=\frac{d}{d y} \int_{y}^{y^{2}} \ln \left(x^{2}+y^{2 answers -
Differentiations
\( f(x)=9 \) \( f(x)=4 x^{4} \) \( y=7 x^{5} \) \( y=4 x^{2}+3 x^{4} \) \( y=x^{2}+7 x=5 \)2 answers -
Differentiations
1. \( y=\frac{4+x}{2 x^{3}} \) 2. \( y=\frac{x^{2}+3 x}{2 \sqrt{x}} \) 3. \( 4 x^{3}(3 x-1) \) 4. \( f(x)=\frac{\left(x^{2}-2\right)^{3}}{1-5 x} \) 5. \( y=\frac{x^{2}}{x+1} \)2 answers -
check if the following statements are true
4. Considera los siguientes vectores de \( R^{3} \) \[ a=(4,6,-3) \quad b=(2,6,4) \quad c=(-1,3,-3) \quad d=(12,30,13) \] Verifica si las siguientes afirmaciones son verdaderas. a) \( d \in G\{a, b, c2 answers -
2 answers