Advanced Math Archive: Questions from September 24, 2023
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Favor de parear paree la columna izquierda con la derecha. Debe de proveer todo el procedimiento para llegar a la respiesta
\[ \begin{array}{l} L^{-1}\left\{\begin{array}{l} e^{-3} \\ s^{3} \end{array}\right\} \\ L^{-1}\left\{\frac{e^{-2 t}}{s(s+1)}\right\} \\ L^{-1}\left\{\begin{array}{c} t e^{-2 x} \\ z^{2}+16 \end{array0 answers -
Selecciona la respuesta correcta: 1. El radio de convergencia de la serie de potencias (+1) Σ a) 0 c) -1 d) 1 e) Ninguno de los anteriores 2. El radio de convergencia de la serie de potencias (-1)(x-
Selecciona la respuesta correcta: 1. E radio de convergencia de la sene de potencias \( \sum_{i=1}^{\infty} \frac{x^{21}}{(n+1)} \) es (5pts) a) 0 b) \( \infty \) c) -1 d) 1 e) Ninguno de los antenore1 answer -
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2. Find the harmonic conjugate v (x, y) of u (x, y) = eª cos y + e³ cos x + xy.
2. Find the harmonic conjugate \( v(x, y) \) of \[ u(x, y)=e^{x} \cos y+e^{y} \cos x+x y \]1 answer -
Find an explicit general solution for 1) \( y^{\prime}=\frac{11}{x} \Rightarrow y= \) 2) \( y^{\prime}=-3 \sin x+7 \cos x \Rightarrow y=3 \cos (\mathrm{x})+7 \sin (\mathrm{x})+C \) 3) \( y^{\prime}=21 answer -
Demuestre si las siguientes series son convergentes o divergentes 1. \( 1+\frac{1}{8}+\frac{1}{27}+\frac{1}{64}+\frac{1}{125}+\cdots \ldots \ldots \ldots \ldots \ldots \ldots \) 2. \( \frac{1}{5}+\fra1 answer -
\( y^{\prime \prime}-4 y^{\prime}+5 y=2 e^{3 x} \) \( y^{\prime \prime}+5 y^{\prime}-6 y=14 e^{x} \)1 answer -
The prices of three products are given by: and the total cost of production of the products is given by C = 20 + 15Q + Q ^ 2 where Q=Q1+Q2+Q3, is the total quantity demanded of the products. Determine
3. Los precios de tres productos están dados por \( \left\{\begin{array}{l}P_{1}=63-4 Q_{1} \\ P_{2}=105-5 Q_{2} \text {, y el costo total de la producción de bs } \\ P_{3}=75-6 Q_{3}\end{array}\rig1 answer -
\( y^{\prime \prime}-4 y^{\prime}+5 y=2 e^{3 x} \) \( y^{\prime \prime}+5 y^{\prime}-6 y=14 e^{x} \)1 answer -
me pueden explicar la demostración, por favor
4.4 Método 3: Cotas de raíces por el método de Newton Dado un polinomio \( f(x)=a_{0}+a_{1} x+a_{2} x^{2}+\ldots .+a_{n-1} x^{n-1}+a_{n} x^{n} \) øn coeficientes reales \( \mathrm{y} \mathrm{a}_{\1 answer -
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13. Algunas veces las ecuaciones diferenciales se resuelven gracias a una idea ingeniosa. Aquí le presentamos un pequeño ejercicio de ingenio. Considere la ecuación \[ \left(x-\sqrt{x^{2}+y^{2}}\ri1 answer -
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15. Obtenga la imagen de las líneas paralelas al eje real bajo la transformación \( f(z)=\operatorname{sen}(z) \)1 answer -
17. Halle la transformación lineal, bilineal o de Möbius, de tal forma que los puntos \( z_{1}, z_{2}, z_{3} \) del plano \( \mathrm{z} \) se apliquen en \( w_{1}, w_{2}, w_{3} \) : a. \( z=(1, i,-11 answer -
is this correct?
Find \( y^{\prime} \) if \( y=\frac{-7}{\sqrt[3]{x}} \) \[ y^{\prime}=\frac{7}{3} x^{-\frac{4}{3}} \]1 answer -
(10 points) e dx +(e* cot(y)+2ycsc(y))dy=0, _y(0)=n Possible answers a. b. C. d. e** sin(y²) + y² = π e* sin(y²) + y = 7 e³ sin(y)+ y² = 7² None of the above
\( (10 \) points \( ) e^{x} d x+\left(e^{x} \cot (y)+2 y \csc (y)\right) d y=0, \quad y(0)=\pi \) Possible answers a. \( \quad e^{x^{2}} \sin \left(y^{2}\right)+y^{2}=\pi \) b. \( \quad e^{x} \sin \le1 answer -
will thumbs up, pls solve
\#9. Solve the IVP: \( x^{2} y^{\prime \prime}+3 x y^{\prime}-3 y=0, \quad y(1)=0, y^{\prime}(1)=-1 \). (a) \( y=-x^{-3} \) (b) \( y=\frac{1}{4} x^{-3}-\frac{1}{4} x \), (e) none of these. (c) \( y=x-1 answer -
will thumbs up, pls solve
\#8. Find a general solution of \( y^{\prime \prime}+6 y^{\prime}+13 y=0 \). \[ \text { (a) } y=c_{1} e^{-4 x}+c_{2} e^{-9 x}, \text { (b) } y=e^{6 x}\left(c_{1}+c_{2} x\right), \text { (c) } y=c_{1}1 answer -
Find the quadratic approximation to \[ f(x, y)=e^{2 x+y^{2}} \] t \( P(0,0) \). 1. \( Q(x, y)=1+y+x y+2 y^{2} \) 2. \( Q(x, y)=1-2 x+2 x y+y^{2} \) 3. \( Q(x, y)=1+x+2 x^{2}+y^{2} \) 4. \( Q(x, y)=1+21 answer -
\( 008 \quad 10.0 \) points Determine \( f_{x y} \) when \[ f(x, y)=x \tan ^{-1}\left(\frac{x}{y}\right) . \] 1. \( f_{x y}=-\frac{x y^{2}}{y^{2}+x^{2}} \) 2. \( f_{x y}=-\frac{x^{2} y}{y^{2}+x^{2}} \3 answers -
will thumbs up, pls solve
\#S Solve the IVP, \( y^{\prime}-y=x+1, y(0)=-1 \). (a) \( y=-1+x e^{x} \), (e) none of these. (b) \( y=-3+2 e^{x}+x \), (c) \( y=-x-2+e^{x} \), (d) \( y=x e^{-x}+2 e^{-x}-3 \),1 answer -
will thumbs up, pls solve
\#S Solve the IVP, \( y^{\prime}-y=x+1, y(0)=-1 \). (a) \( y=-1+x e^{x} \), (e) none of these. (b) \( y=-3+2 e^{x}+x \), (c) \( y=-x-2+e^{x} \), (d) \( y=x e^{-x}+2 e^{-x}-3 \),1 answer -
pls solve will thumbs up
\#9. Solve the IVP: \( x^{2} y^{\prime \prime}+3 x y^{\prime}-3 y=0, \quad y(1)=0, y^{\prime}(1)=-1 \). (a) \( y=-x^{-3} \) (b) \( y=\frac{1}{4} x^{-3}-\frac{1}{4} x \), (e) none of these. (c) \( y=x-1 answer