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Advanced Math Archive: Questions from July 26, 2022

$(c) (14 pts) Solve initial value problem \[ \left\{\begin{array}{c} \left(\sin \left(x+y^{2}\right)+e^{3 x}-7\right) d x+\lef$

(c) (14 pts) Solve initial value problem \[ \left\{\begin{array}{c} \left(\sin \left(x+y^{2}\right)+e^{3 x}-7\right) d x+\left(2 y \sin \left(x+y^{2}\right)+y-1\right) d y=0 \\ y(0)=0 \end{array}\righ

3 answers
Para las transformación dada: demuestre que son lineales, encuentre el nucleo, imagen, rango y nulidad T:R2->R2; Tv=Av, donde A esta dado por la matriz A= cos (Theta) -sen(Theta) sen(Thet

1 answer
If not linear transformation, please show why. Thanks!
4. Which of the following are linear transformations? a. $ \mathrm{L}(\mathrm{x}, \mathrm{y})=(\mathrm{x}, \mathrm{y}, \mathrm{x}+\mathrm{y}) $ b. $ L(x, y, z)=(x+y, 1, x-z) $ c. \( L(x, y)=\left(

1 answer
$The graph shown is of the function a) $ y=\frac{1}{\tan x} $ b) $ y=\frac{1}{\sec x} $ C) $ y=\frac{1}{\sin x} $ d) $$

The graph shown is of the function a) \( y=\frac{1}{\tan x} $ b) $ y=\frac{1}{\sec x} $ C) $ y=\frac{1}{\sin x} $ d) $ y=\frac{1}{\cos x} $

3 answers
Compute total differentials dy.
$ y=\left(x_{1}-1\right) /\left(x_{2}+1\right) $ $ y=x_{1} x_{2}^{2}+\frac{x_{1}^{2}-x_{2}^{2}}{x_{1}+1} $

3 answers
Find a general solution for y''' - y" + 4y' - 4y = 0.

1 answer
$Let\ A = \begin{pmatrix} 2 & -3\\ 1 &2 \end{pmatrix}, B = \begin{pmatrix} -1& 2 & -3\\ 0& 5 & 4\\ \end{pmatrix}. Find\ AB,\ BA, if possible.$

$Let $ A=\left(\begin{array}{cc}2 & -3 \\ 1 & 2\end{array}\right), B=\left(\begin{array}{ccc}-1 & 2 & -3 \\ 0 & 5 & 4\end{arr$

Let \( A=\left(\begin{array}{cc}2 & -3 \\ 1 & 2\end{array}\right), B=\left(\begin{array}{ccc}-1 & 2 & -3 \\ 0 & 5 & 4\end{array}\right) $. Find $ A B, B A $, ifpossible.

1 answer
$Evaluate the double integral. \[ \iint_{D} e^{-y^{2}} d A, \quad D=\{(x, y) \mid 0 \leq y \leq 7,0 \leq x \leq y\} \]$

Evaluate the double integral. \[ \iint_{D} e^{-y^{2}} d A, \quad D=\{(x, y) \mid 0 \leq y \leq 7,0 \leq x \leq y\} \]

3 answers
$$ \int_{C} \mathbf{F} \cdot d \mathbf{r} $ $ \mathbf{F}(x, y)=x \mathbf{i}+y \mathbf{j} $ $ \quad C: \mathbf{r}(t)=(7 t+$

\( \int_{C} \mathbf{F} \cdot d \mathbf{r} $ $ \mathbf{F}(x, y)=x \mathbf{i}+y \mathbf{j} $ $ \quad C: \mathbf{r}(t)=(7 t+2) \mathbf{i}+t \mathbf{j}_{r} \quad 0 \leq t \leq 1 $

1 answer
$Solve the following IVPs: A. $ y^{\prime \prime}+3 y^{\prime}=0, y(0)=3, y^{\prime}(0)=1 $. B. $ x y^{\prime}+y=6, y(1)=3$

Solve the following IVPs: A. \( y^{\prime \prime}+3 y^{\prime}=0, y(0)=3, y^{\prime}(0)=1 $. B. $ x y^{\prime}+y=6, y(1)=3 $. C. $ y(\cos x-y) d x=(2 x y-\sin x) d y, y(\pi)=1 $. D. \( y^{\prime}

1 answer
$Which of the following vector-fields on $ \mathbb{R}^{3} $ are conservative? Select all conservative vector-fields. Sélecti$

$\[ \vec{H}=e^{x} \hat{i}+\cos y \hat{j}+e^{z^{2}} \hat{k} \] b) \[ \vec{L}=e^{x} \hat{i}+x \cos y \hat{j}+e^{z^{2}} \hat{k} \$

$\[ \vec{A}=2 y z \hat{i}+3 x z \hat{j}+7 x y \hat{k} \] d) \[ \vec{F}=\left(x^{2}-y^{2}\right) \hat{i}+2 x y \hat{j}-z \hat{k$

Which of the following vector-fields on $ \mathbb{R}^{3} $ are conservative? Select all conservative vector-fields. Sélectionnez 2 réponse(s) correcte(s) a) \[ \vec{H}=e^{x} \hat{i}+\cos y \hat{j}

3 answers

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Advanced Math Archive: Questions from July 26, 2022

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