Advanced Math Archive: Questions from May 07, 2023
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1. Find the general solution for the following homogenous differential equations: 1. \( y^{\prime \prime}-6 y^{\prime}+10 y=0 \). 2. \( y^{\prime \prime}-3 y^{\prime}=0 \). 3. \( y^{\prime \prime}+6 y2 answers -
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DIFFER EQ
ive: \( \frac{y^{\prime \prime}}{y^{\prime}}=\frac{1}{x} \ln \left(\frac{y^{\prime}}{x}\right) \)2 answers -
Utilizar integrales múltiples para calcular el volumen Using Multiple Integrals to Calculate Volume
\begin{tabular}{|l|l|l|} \hline \multicolumn{1}{|c|}{ Figura } & \multicolumn{1}{c|}{ Ecuación } & \multicolumn{1}{c|}{ Rangos } \\ \hline Cilindro & \( \left(x^{\wedge} 2 / 2^{\wedge} 2\right)+\left2 answers -
5. Suponer que \( f \) es diferenciable en \( [a, b], f(a)=0 \) y que existe un número real no negativo \( C \) tal que \[ \left|f^{\prime}(x)\right| \leq C|f(x)| \] para cada \( x \in[a, b] \). Demo2 answers -
Suponer que a) \( f \) es continua para \( x \geq 0 \), b) \( f^{\prime}(x) \) existe para \( x>0 \), c) \( f(0)=0 \), d) \( f^{\prime} \) es monótona creciente. Defina la función \( g \) con domini2 answers -
Suponga que \( f \) está definida en \( (-1,1) \) y que \( f^{\prime}(0) \) existe, también que \( \left\{\alpha_{n}\right\}_{n=0}^{\infty} \) y \( \left\{\beta_{n}\right\}_{n=0}^{\infty} \) son dos2 answers -
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g) \( \frac{d^{2} y}{d t^{2}}+4 y=-8 t \sin 2 t, \quad y(0)=\frac{d y}{d t}(0)=0 \) Ans: \( y=t^{2} \cos 2 t-\frac{1}{2} t \sin 2 t \).2 answers -
I need the volume for each equation using integrals
Utilizar integrales múltiples para calcular el volumen Using Multiple Integrals to Calculate Volume \begin{tabular}{|l|l|l|} \hline \multicolumn{1}{|c|}{ Figure } & \multicolumn{1}{c|}{ Equations }2 answers -
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1. Solve the IVP \[ y^{\prime \prime}+y=f(t), \quad \quad \text { subject to } y(0)=y^{\prime}(0)=0 \] where \[ f(t)=\left\{\begin{array}{cc} 2 \sin t, & 0 \leq t2 answers -
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Find the lenght of the curve of the next equations: from t=0 to t=2
\( r(t)=t i+\frac{2}{3} \sqrt{2} t^{3 / 2} j+\frac{1}{2} t^{2} k \quad \) desde \( t=0 \) hasta \( t=2 \) 1. Hallar la longitud de la curva \[ r(t)=(t \operatorname{sen} t+\cos t) i+(t \cos t-\operat2 answers -
Let \( \vec{F}(x, y, z)=2 x^{2} \vec{i}-\sin (x y)(\vec{i}+\vec{j}) \). Calulate the divergence: \( \operatorname{div} \vec{F}(x, y, z)= \)2 answers -
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Problem 11. Let \[ f(x)=\sum_{k=1}^{\infty} \frac{\cos (k x)}{k^{2}} . \] Prove that \[ \int_{0}^{\pi / 2} f(x) d x=\sum_{k=0}^{\infty} \frac{(-1)^{k}}{(2 k+1)^{3}} \]2 answers