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Advanced Math Archive: Questions from January 05, 2023

$\begin{array}{l} \left(\frac{1}{x}+2 x y^{2}\right) d x+\left(2 x^{2} y-\cos y\right) d y=0 \\ y(1=)+1, x>0 \end{array}$

\[ \begin{array}{l} \left(\frac{1}{x}+2 x y^{2}\right) d x+\left(2 x^{2} y-\cos y\right) d y=0 \\ y(1=)+1, x>0 \end{array} \] Solve please

1 answer
$c. Valor 30 pts. 1. $ \lim _{x \rightarrow 1} \frac{x^{2}-1}{x-1} $ 6. $ \lim _{x \rightarrow-2} \frac{x^{2}-4}{x+2} $ 2.$

c. Valor 30 pts. 1. $ \lim _{x \rightarrow 1} \frac{x^{2}-1}{x-1} $ 6. $ \lim _{x \rightarrow-2} \frac{x^{2}-4}{x+2} $ 2. $ \lim _{x \rightarrow 0} \frac{x^{2}-x}{x} $ 7. \( \lim _{x \rightarrow

2 answers
Resolver con el método de separación de variables
Resuelva la ecuación del calor $ k u_{x x}=u_{t} $ donde \( 0

1 answer
Pls don´t answer if you don´t know how to solve the problem
7. Una barra de $ 50 \mathrm{~cm} $ de longitud está inmersa en vapor. Su temperatura inicial está dada por \( f(x)=\left\{\begin{array}{ccc}4 x & \text { si } & 0 \leq x

0 answers
Resolver por separación de variables, no por otro método.
2. Considere la ecuación $ k \frac{\partial^{2} u}{\partial x^{2}}=\frac{\partial u}{\partial t} $. (a) ¿De qué tipo es? (b) Verifique si la función \[ u(x, t)=\frac{1}{\sqrt{4 \pi k t}} e^{-x^{

2 answers
$3. Find $ u_{x} $ and $ u_{y} $ for the following functions. (a) $ u(x, y)=5 x^{2} y^{3}-7 x^{3} y^{5} $. (b) $ u(x, y$

3. Find \( u_{x} $ and $ u_{y} $ for the following functions. (a) $ u(x, y)=5 x^{2} y^{3}-7 x^{3} y^{5} $. (b) $ u(x, y)=x^{2} y+x \sin y $. (c) $ u(x, y)=\sqrt{2 x^{2}+y^{2}} $. (d) \( u(x,

2 answers
$5. Find $ f_{x} $ and $ f_{y} $ for the following functions. (a) $ f(x, y)=y \sqrt{x^{2}-y^{2}} $. (b) $ f(x, y)=x e^{$

5. Find \( f_{x} $ and $ f_{y} $ for the following functions. (a) $ f(x, y)=y \sqrt{x^{2}-y^{2}} $. (b) $ f(x, y)=x e^{2 x^{2}+y^{2}} $. (c) $ f(x, y)=y \cos (4 x+y) $ (d) \( f(x, y)=e^{x-y}

2 answers

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Advanced Math Archive: Questions from January 05, 2023

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