Advanced Math Archive: Questions from November 27, 2022
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Explicar paso a paso. y(x, 0) = f(x), dy/dt(x, 0) = 0, y (1, t) = 0 y(x, t) is definied for 0 ≤ x ≤ 1, t > 0.
6. Resuelva el problema de valores de frontera \[ \frac{\partial}{\partial x}\left(x \frac{\partial y}{\partial x}\right)=\frac{\partial^{2} y}{\partial t^{2}} \] Dado que \( y(x, 0)=f(x), y_{t}(x, 0)0 answers -
pls
4. Use transformaciones en gráficas conocidas (funciones de potencia) para dibujar la gráfica de cada una dee las siguientes. En cada caso indique la función conocida que está usando. a. \( f(x)=12 answers -
2 answers
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2 answers
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Number #16
EXERCISES \( 4.4 \) Answers to selected odd-numbered problems begin on page ANS-5. In Problems 1-26 solve the given differential equation by undetermined coefficients. 16. \( y^{\prime \prime}-5 y^{\p2 answers -
Number 32
In Problems 31-40 use the Laplace transform to solve the given initial-value problem. 31. \( \frac{d y}{d t}-y=1, \quad y(0)=0 \) 32. \( 2 \frac{d y}{d t}+y=0, \quad y(0)=-3 \) 33. \( y^{\prime}+6 y=e2 answers -
3. Calcula el área debajo de las siguientes curvas, en el intervalo indicado, usando método rectangular indicado \( \mathrm{y} \) de forma exacta. a. \( y=x^{2}+3 ;[-3,1] \) usando 4 rectángulos po2 answers -
3.2
Evaluate \( \iiint_{E}(x+y-4 z) d V \) where \[ E=\left\{(x, y, z) \mid-4 \leq y \leq 0,0 \leq x \leq y, 01 answer -
Number 1 only
In Exercises 1-20 solve the initial value problem. Where indicated by \( \quad \), graph the solution. 1. \( y^{\prime \prime}+3 y^{\prime}+2 y=6 e^{2 t}+2 \delta(t-1), \quad y(0)=2, \quad y^{\prime}(2 answers -
Number 6
In Exercises 1-20 solve the initial value problem. Where indicated by \( \quad \), graph the solution. 1. \( y^{\prime \prime}+3 y^{\prime}+2 y=6 e^{2 t}+2 \delta(t-1), \quad y(0)=2, \quad y^{\prime}(2 answers -
Numbers 10 and 15
In Exercises 1-20 solve the initial value problem. Where indicated by \( \quad \), graph the solution. 1. \( y^{\prime \prime}+3 y^{\prime}+2 y=6 e^{2 t}+2 \delta(t-1), \quad y(0)=2, \quad y^{\prime}(2 answers -
2 answers
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Solve the following DE using Laplace Transform: 1. \( y^{\prime \prime}+y=e^{-t} \quad y(0)=0, y^{\prime}(0)=0 \) 2. \( y^{\prime \prime}-2 y^{\prime}=-4 \quad y(0)=0, y^{\prime}(0)=4 \) 3. \( y^{\pri2 answers -
\( \neg \forall x \forall y A(x, y) \) has the same truth value as \( \forall x \exists y \neg A(x, y) \) \( \exists x \neg \forall y A(x, y) \) \( \forall x \forall y \neg A(x, y) \) \( \forall x \ne1 answer -
Considere el siguiente circuito, donde: \( E(t)=68 \) volts; \( L 1=8 \mathrm{H} ; L 2=8 \mathrm{H} ; R=14 \) ohms, Además las corrientes iniciales son cero, es decir, \( i_{1}(0)=0 ; i_{2}(0)=0 \) L2 answers -
Find the exact values of \( \sin ^{-1} \frac{1}{2} \) and \( \tan ^{-1} 1 \). \[ \begin{array}{l} \sin ^{-1} \frac{1}{2}= \\ \tan ^{-1} 1= \end{array} \]2 answers -
Solve the following DE using Laplace Transform: 1. \( y^{\prime \prime}+y=e^{-t} \) \( y(0)=0, y^{\prime}(0)=0 \) 2. \( y^{\prime \prime}-2 y^{\prime}=-4 \) \( y(0)=0, y^{\prime}(0)=4 \) 3. \( y^{\pri2 answers -
Confluent Hypergeometric
Using the Frobenius method, show that the solution of the confluent hypergeometric equation \[ x y^{\prime \prime}+(c-x) y^{\prime}-a y=0, \] has a solution given by the expansion \[ y(x)=c_{0} \sum_{1 answer -
2 answers
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1. (6 ptos c/u.) Considere el grupo \( (\mathbb{Z},+) \) y los subgrupos \( \langle 5\rangle \) y \( \langle 11\rangle \) de \( \mathbb{Z} \). Sea \[ \begin{aligned} \varphi: \mathbb{Z} & \longrightar0 answers -
2. Sean \( (G, \cdot) \) y \( (H, *) \) dos grupos y sea \( f \in \operatorname{Hom}(G, H) \). Muestre lo siguiente: i. (6 ptos.) \( f \) es monomorfismo si y sólo si \( \operatorname{ker}(f)=\left\{2 answers -
3. (5 ptos c/u.) Considere el conjunto de los números enteros \( (\mathbb{Z}, *, \circ) \) con una nueva operación suma y una nueva operación multiplicación dadas por: \[ a * b=a+b+1, \quad a \cir2 answers -
2 answers
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19,23
In Exercises 17-24, compute the double integral of \( f(x, y) \) over the domain \( \mathcal{D} \) indicated. 17. \( f(x, y)=x^{3} y ; \quad 0 \leq x \leq 5, \quad x \leq y \leq 2 x+3 \) 18. \( f(x, y1 answer