Advanced Math Archive: Questions from November 28, 2022
-
1 answer
-
Let \( \gamma(t)=e^{i t} \), for \( 0 \leq t \leq 2 \pi \). Calculate \[ \int_{\gamma} f(z) d z \] when: (a) \( f(z)=z^{2} e^{-1 /\left(z^{3}\right)} \) (b) \( f(z)=\left(z^{2}+z\right) \cos (1 / z) \2 answers -
(b) Find a potential field function for \( \vec{G}(x, y)=x y \vec{i}+(x+y) \vec{j}) \), or prove none exists. (c) If \( H(x, y, z)=x y z \vec{i}+\sin (x y) \vec{j}-\cos (y z) \vec{k} \), compute \( \n2 answers -
4. Show \[ \int_{-\infty}^{\infty} \frac{x^{2}}{\left(x^{2}+9\right)^{2}} d x=\frac{\pi}{6} \] providing all the necessary details.2 answers -
2 answers
-
Solve the equations. (a) \( y^{\prime \prime}-4 y^{\prime}+3 y=0 \) (b) \( y^{\prime \prime \prime}+6 y^{\prime \prime}+9 y^{\prime}=0 \) (c) \( y^{\prime \prime}+25 y=0 \)2 answers -
Solve the equations. (a) \( y^{\prime \prime}-4 y^{\prime}+3 y=0 \) (b) \( y^{\prime \prime \prime}+6 y^{\prime \prime}+9 y^{\prime}=0 \) (c) \( y^{\prime \prime}+25 y=0 \)2 answers -
4. Solve the equations. (a) \( y^{\prime \prime}-4 y^{\prime}+3 y=0 \) (b) \( y^{\prime \prime \prime}+6 y^{\prime \prime}+9 y^{\prime}=0 \) (c) \( y^{\prime \prime}+25 y=0 \)2 answers -
Solve the equations. (a) \( y^{\prime \prime}-4 y^{\prime}+3 y=0 \) (b) \( y^{\prime \prime \prime}+6 y^{\prime \prime}+9 y^{\prime}=0 \) (c) \( y^{\prime \prime}+25 y=0 \)2 answers -
2 answers
-
Solve the IVP: \( \left(1+x^{2}\right) y^{\prime}+2 x y=f(x), y(0)=0 \), where \[ f x)=\left\{\begin{array}{ll} x, & 0 \leq x2 answers -
\( \left(1+x^{2}\right) y^{\prime}+2 x y=f(x), y(0)=0 \), where \[ f x)=\left\{\begin{array}{ll} x, & 0 \leq x2 answers -
*32. Denotemos por \( R \) la región dentro de \( x^{2}+y^{2}=1 \) pero fuera de \( x^{2}+y^{2}=2 y \) con \( x \geq 0, y \geq 0 \) (a) Esbozar esta región. (b) Sea \( u=x^{2}+y^{2}, v=x^{2}+y^{2}-21 answer -
solve the differential equation or initial value problem
6. \( y^{\prime \prime}+4 y^{\prime}+4 y=\frac{1}{t^{2} \mathrm{e}^{2 t}} \) 7. \( y^{\prime \prime}+y=\left\{\begin{array}{rrr}1, & 0 \leq t2 answers -
Show \[ \int_{-\infty}^{\infty} \frac{x^{2}}{\left(x^{2}+9\right)^{2}} d x=\frac{\pi}{6} \] providing all the necessary details.2 answers -
solve only 12 and 14
12. \( y^{\prime \prime}+y=\delta\left(t-\frac{\pi}{2}\right)+\delta\left(t-\frac{3 \pi}{2}\right) ; y(0)=y^{\prime}(0)=0 \). 13. \( y^{\prime \prime}+2 y^{\prime}=\delta(t-1) ; y(0)=0, y^{\prime}(0)=2 answers -
show all steps pls
oolve \( y^{\prime \prime}+2 y^{\prime}+10 y=-9 \delta(t-10)+12 \delta(t-15), y(0)=1, y^{\prime}(0)=3 \)1 answer -
2 answers
-
Una masa de 100 gramos se susponde de un extremo de un resorte y el otro extremo se suspende de un soporte fijo dejando que el sistema alcance el reposo. La constante del resorte es \( 196 \mathrm{gr}0 answers -
Find an explicit general solution for 1) \( y^{\prime}=\frac{4}{x} \Rightarrow y= \) 2) \( y^{\prime}=-4 \sin x+7 \cos x \Rightarrow y= \) 3) \( y^{\prime}=-6 e^{x} \Rightarrow y= \)2 answers -
Problem 3. Prove that \( B \subsetneq A \) for: \[ \begin{array}{c} A=\left\{(x, y) \in \mathbb{R}^{2}:|x+y|2 answers -
y′′ + 4y′ + 5y = δ(t−2π); y(0)=y′(0)=0
\( y^{\prime \prime}+4 y^{\prime}+5 y=\delta(t-2 \pi) ; y(0)=y^{\prime}(0)=0 \)2 answers -
4. Solve using Laplace Transforms. \( y^{\prime \prime}+5 y^{\prime}+4 y=\left\{\begin{array}{l}0 \\ 1\end{array}\right]+ \) if \( _{\text {if }} \quad \begin{array}{r}0 \leq t2 answers -
Solve the following IVP using the Laplace transform: \[ y^{\prime \prime}-2 y^{\prime}+y=t^{2} e^{t}, \quad y(0)=1, y^{\prime}(0)=2 \]2 answers -
Para la sigueinte Matriz A encuentre el polinomio.
3. Para la siguiente matriz \( A \) encuentre el polinomio \( \psi(\lambda) \) que es igual a \( f(\lambda)=\lambda^{11} \) en el espectro de \( A \) y calcule \( A^{11} \) evaluando \( \psi(A) \) \[0 answers -
Consider linear transformation L(x1, x2, x3) = (x1, x1 + x2 - x3) from R3 to R2. a. Prove that L is a linear transformation. b. Find a basis for the kernel of L. c. Find a basis for the image of L. d.
1. Considerar la transformación lineal \( L\left(x_{1}, x_{2}, x_{3}\right)=\left(x_{1}, x_{1}+x_{2}-x_{3}\right) \) de \( \mathbb{R}^{3} \) a \( \mathbb{R}^{2} \). a. (8\%) Demostrar que \( L \) es2 answers -
Considerar la transformación lineal \( L\left(x_{1}, x_{2}, x_{3}\right)=\left(x_{1}, x_{1}+x_{2}-x_{3}\right) \) de \( \mathbb{R}^{3} \) a \( \mathbb{R}^{2} \) a. Demostrar que \( \mathrm{L} \) es u2 answers -
Considerar la base \( U \) de \( \mathbb{R}^{3} \) dada por \( u_{1}=(1,0,0), u_{2}=(0,1,0) \) y \( u_{3}=(1,1,0) \) y la base \( / \) de \( \mathbb{R}^{2} \) dada por \( v_{1}=(1,0) \) y \( v_{2}=(1,0 answers -
Need help with Question 8
In Problems 1-8, determine the first three nonzero terms in the Taylor polynomial approximations for the given initial value problem. 1. \( y^{\prime}=x^{2}+y^{2} ; \quad y(0)=1 \) 2. \( y^{\prime}=y^2 answers -
is a linear transformation (true or false)
\( L\left(x_{1}, x_{2}\right)=\left(x_{1}, x_{2}+2\right) \) es una transformación lineal de \( \mathbb{R}^{2} \) en \( \mathbb{R}^{2} \) ? (cierto o falso)2 answers -
Evaluate \( V=\iint_{\mathcal{R}} \sqrt{9+x^{2}+y^{2}} d A \), where \( \mathcal{R}=\left\{(x, y) \mid 0 \leq x \leq 4,0 \leq y \leq \sqrt{16-x^{2}}\right\} \).2 answers -
Calculate \( \iint_{S} f(x, y, z) d S \) For \[ x^{2}+y^{2}=4, \quad 0 \leq z \leq 1 ; \quad f(x, y, z)=e^{-z} \] \[ \iint_{S} f(x, y, z) d S= \]2 answers -
2 answers
-
Solve the differential equation using the series method of y′′ + xy′ − 2y = ex, and obtain a polynomial of at least degree 5, if y(0) = y′ (0) = 0.
e (12 puntos) Resuelva la ecuación diferencial usando el método de series de \( y^{\prime \prime}+x y^{\prime}-2 y=e^{x} \), y obtenga un polinomio de por lo menos grado 5 , si \( y(0)=y^{\prime}(0)2 answers -
Solve the IVP \[ \vec{y}^{\prime}=\frac{1}{6}\left(\begin{array}{cc} 7 & 2 \\ -2 & 2 \end{array}\right) \vec{y}, \quad \vec{y}(0)=\left(\begin{array}{c} 0 \\ -3 \end{array}\right) \]2 answers -
Solve the following differential equations: a. \( y^{\prime \prime}-y^{\prime}-2 y=0 \) b. \( y^{\prime \prime}-7 y^{\prime}=0 \) c. \( y^{\prime \prime}-0.04 y=0 \)2 answers -
I. Consider the set of vectors w_1=(2,-2,1),w_2=(-1,2,0), w_3=(3,-2,λ).w_4=(-5,6,-2) where λ is a real number. a) Find a value for λ such that the dimension of span{w_1, w_2,w_3,w_4} is 3. Then dec
I. Considere el conjunto de vectores \[ w_{1}=(2,-2,1), \quad w_{2}=(-1,2,0), \quad w_{3}=(3,-2, \lambda) . w_{4}=(-5,6,-2) \] donde \( \lambda \) es un número real. a) Encuentre un valor para \( \la2 answers -
(c) If \( H(x, y, z)=x y z \vec{i}+\sin (x y) \vec{j}-\cos (y z) \vec{k} \), compute \( \nabla \times H(x, y, z) \).2 answers -
10. Sea \( M(n, \mathbb{R}) \) el conjunto de matrices \( n \times n \) con entradas reales. (a) Demuestre que \( M(n, \mathbb{R}) \) es un espacio vectorial isomorfo a \( \mathbb{R}^{n^{2}} \). (b) P2 answers -
Para simular una población se utiliza el modelo logístico: \[ \frac{d p}{d t}=k_{g m}\left(1-\frac{p}{p_{\text {máx }}}\right) p \] donde \( \mathrm{p} \) = población, \( \mathrm{k}_{\mathrm{gm}}0 answers -
Solve L, P, and Q pls
5. Solve the following systems of equations: (a) \( x^{\prime}=y \) \[ y^{\prime}=-x+2 y \] (b) \( x^{\prime}+y^{\prime}-2 x-4 y=e^{4 t} \) \[ x^{\prime}+y^{\prime}-y=e^{4 t} \] (c) \( 5 x^{\prime}+y^2 answers -
3) Find a general solution. (a) \( 2 y^{\prime \prime \prime}+5 y^{\prime \prime}-2 y^{\prime}-5 y=7 e^{x}-8 e^{3 x} \) (b) \( y^{\prime \prime \prime}+9 y^{\prime}=9 \cos (3 x)+27 x^{2}-9 x+18 \)2 answers -
2 answers
-
Let \[ f(x, y)=\left\{\begin{array}{ll} 0 & \text { if } y \leq 0 \text { or } y \geq x^{4} \\ 1 & \text { if } 02 answers