Advanced Math Archive: Questions from April 20, 2023
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Find the inttial value of the ODE \[ (\cos x)\left(1-6 y^{2}\right) d y=y \sin x d x \quad y(0)=1 \]2 answers -
Determine whether or not the set is compact \[ A=\{(x, y) \in \mathbb{R}: y=\sin (1 / x), x \neq 0\} \cup\{(0, y):-1 \leq y \leq 1\} \]2 answers -
Find \( \frac{\partial z}{\partial x}, \frac{\partial z}{\partial y}, \frac{\partial^{2} z}{\partial x \partial y}, \frac{\partial^{2} z}{\partial x^{2}}, \frac{\partial^{2} z}{\partial y^{2}} \) and2 answers -
Find \( \frac{\partial z}{\partial x}, \frac{\partial z}{\partial y}, \frac{\partial^{2} z}{\partial x \partial y}, \frac{\partial^{2} z}{\partial x^{2}}, \frac{\partial^{2} z}{\partial y^{2}} \) and2 answers -
Exercise 3.21 Find the horizon cones of the following sets: (i) \( F:=\left\{(x, y) \in \mathbb{R}^{2} \mid y \geq x^{2}\right\} \). (ii) \( F:=\left\{(x, y) \in \mathbb{R}^{2}|y \geq| x \mid\right\}2 answers -
Please solve
\( \begin{array}{l}p=2 x+y \text { subject } \\ x+2 y \geq 16 \\ 2 x+y \leq 16 \\ x+y \leq 5 \\ x \geq 0, y \geq 0\end{array} \)2 answers -
3. La curva cerrada \( \Gamma \) consiste de 4 segmentos recorridos en sentido positivo con vértices en \( (1,2),(3,2)) \), \( (3,5),(1,5) \) Calcule \[ \int_{\Gamma} x^{2} d x+\left(y e^{-y^{2}}+x^{2 answers -
4. Encontrar el area de la parte de la superficie \[ y=4 x+z^{2} \] que está entre los planos \[ x=0, x=4, \quad \text { y } z=0, z=1 \]2 answers -
I need b, c ,d and e
Evalúa las siguientes integrales de línea, aquí considera que \( \mathrm{C} \) es una curva cualquiera de \( A \) a \( B \). a) \( \int_{C} e^{x} \operatorname{sen}(y) d x+e^{x} \cos (y) d y \) don2 answers -
4) Halla un campo vectorial conservativo que tenga la función potencial dada en cada uno de los siguientes incisos: a) \( \phi(x, y)=2 x^{3}-3 x^{2} y+x y^{2}-4 y^{3} \) b) \( \phi(x, y, z)=x^{2} y e2 answers -
Verifica que los siguientes campos sean conservativos, encuentra una función potencial para cada caso: a) \( \boldsymbol{F}(x, y, z)=\left(z e^{x}+e^{y}\right) \boldsymbol{i}+\left(x e^{y}-e^{z}\righ2 answers -
(b) \( y^{\prime \prime}+9 y=\cos 3 t ; y(0)=1, y^{\prime}(0)=-1 \) (c) \( y^{\prime \prime}+y^{\prime}+y=\sin t ; y(0)=0, y^{\prime}(0)=0 \) (d) \( y^{\prime \prime \prime}-y^{\prime \prime}-y^{\prim2 answers -
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(1 point) Find the Jacobian. \( \frac{\partial(x, y, z)}{\partial(s, t, u)} \), where \[ x=3 t-2 s+4 u, y=s+2 t-4 u, z=-(s+5 t+5 u) \] \[ \frac{\partial(x, y, z)}{\partial(s, t, u)}= \]2 answers -
(i) \( \int \frac{x^{2}+8 x-3}{x\left(x^{2}+3 x\right)} d x \) (ii) \( \int_{0}^{\frac{\pi}{4}} \frac{x \sin x}{\cos ^{3} x} d x \) (iii) \( \int_{0}^{+\infty} x^{3} e^{-x^{2}} d x \) (iv) \( \int_{1}2 answers -
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Only 16a and 16b is needed please show all work.
15-16 Confirm that \( \phi \) is a potential function for \( \mathbf{F}(\mathbf{r}) \) on some region, and state the region. 15. (a) \( \phi(x, y)=\tan ^{-1} x y \) \( \mathbf{F}(x, y)=\frac{y}{1+x^{22 answers -
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