Advanced Math Archive: Questions from October 29, 2022
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2 answers
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5) \( 16 y^{\prime \prime}+16 y^{\prime}-21 y=0 \) 6) \( y^{\prime \prime}+12 y^{\prime}+36 y=0, \quad y(0)=\frac{1}{3}, y^{\prime}(0)=-\frac{3}{2} \).2 answers -
solve 22
17-22 Use appropriate forms of the chain rule to find \( \partial z / \partial u \) and \( \partial z / \partial v \) 17. \( z=8 x^{2} y-2 x+3 y ; x=u v, y=u-v \) 18. \( z=x^{2}-y \tan x ; x=u / v, y=2 answers -
(13 points) Let y be the solution of the initial value problem \[ y^{\prime \prime}+y=-\sin (2 x), y(0)=0, y^{\prime}(0)=0 \] The maximum value of \( y \) is2 answers -
1 answer
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Fill in the blanks
\( L\left\{e^{-7 t}\right\}= \) \( L\{\sin 2 t\}= \) \( L\left\{t^{5}\right\}= \) \( L\{\cos \sqrt{3} t\}= \) \( L\left\{\sinh \frac{1}{2} t\right\}= \) Instrucciones: Arrastre las respuestas en los e2 answers -
0 answers
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\[ \mathbb{C}\left[t^{2}, t^{3}\right]:=\left\{f\left(t^{2}, t^{3}\right) \mid f(x, y) \in \mathbb{C}[x, y]\right\}=\left\{a_{0}+a_{2} t^{2}+a_{3} t^{3}+a_{4} t^{4}+\cdots+a_{n} t^{n} \mid a_{i} \in \0 answers -
2 answers
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Use power series to solve the initial-value problem \[ \left(x^{2}-4\right) y^{\prime \prime}+8 x y^{\prime}+6 y=0, \quad y(0)=1, \quad y^{\prime}(0)=0 \] Answer \( y=\sum_{n=0}^{\infty} \quad x^{2 n}2 answers -
2 answers
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problems 53 and 56 determine all critical points and all domain endpoints for each function.
50. \( f(x)=\frac{x^{2}}{x-2} \) 51. \( y=x^{2}-32 \sqrt{x} \) 52. \( g(x)=\sqrt{2 x-x^{2}} \) 53. \( y=\ln (x+1)-\tan ^{-1} x \) 54. \( y=2 \sqrt{1-x^{2}}+\sin ^{-1} x \) 55. \( y=x^{3}+3 x^{2}-24 x+2 answers -
Solve the following differential equations in partial derivatives. (what book are these problems from?)
1. \( \frac{\partial^{2} u}{\partial y^{2}}=x \cos \pi y \quad \) Respuesta: \( u(x, y)=-\frac{x}{\pi^{2}} \cos \pi y+y f(x)+g(x) \) 2. \( \frac{\partial^{2} R}{\partial x \partial t}=3 \frac{\partial2 answers -
3. Fije \( n \geq 1 \). Muestre que las \( n \)-raíces de la unidad \( w_{0}, \ldots, w_{n-1} \) satisface: a) \( \left(z-w_{0}\right)\left(z-w_{1}\right) \cdots\left(z-w_{n-1}\right)=z^{n}-1 \). b)2 answers -
Determine all values of the following: (a) \( 2^{1-i} \); (b) \( (\cos i)^{i} \); (c) \( (1+i)^{1+i} \); (d) \( i^{\sin i} \)2 answers -
La integral \( V=\int_{0}^{5} \int_{0}^{c} f(x, y) d y d x \) representa el volumen de un sólido, donde \( f(x, y)=9-x-y \geq 0 \) y \( c>0 . \mathrm{Si} \) \( V=47 \) unidades cúbicas, determine \(2 answers -
Encontrar los valores extremos de la función \[ f(x, y)=\frac{3}{2} x^{2}+\frac{7}{2} y^{2}-9 x-21 \] en la región acotada por las rectas \( y=x+3, x=6 y \) \( y=0 \) Máximo Absoluto: \( f_{\max }=2 answers -
\( \operatorname{Sean} z(x, y)=f(u, v) \) \( u=9 x^{2}, v=3 x y \); siendo una función diferenciable. Determina \( D=-4 \frac{\partial^{2} z}{\partial x^{2}}+\frac{7 y}{x} \frac{\partial^{2} z}{\part2 answers -
2 answers
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Solve the following differential equations in partial derivatives. P.02, P.03, P.04 (what book are these problems from?)
2. \( \frac{\partial^{2} R}{\partial x \partial t}=3 \frac{\partial R}{\partial t}+2 t \) sujeta a \( \frac{\partial R}{\partial t}(0, t)=t^{2}-2 t, R(x, 0)=x+3 e^{-x} \) Respuesta: \( R=-\frac{1}{3}2 answers -
(2 points) Let \( x, y, z \) be (non-zero) vectors and suppose \( w=-12 x-6 y+2 z \). If \( z=4 x+2 y \), then \( w= \) Using the calculation above, mark the statements below that must be true. A. \(2 answers