Advanced Math Archive: Questions from February 28, 2023
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(f) \( 3 x+y-2+y^{\prime}(x-1)=0 \) (g) \( \left(t^{2} x^{2}-1\right) x^{\prime}+2 t x^{3}=0 \), haciendo \( x=z^{\alpha} \)2 answers -
2 answers
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1 answer
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2 answers
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3. Convert the following functions \( f(x, y) \) into polar coordinate functions \( g(r, \theta) \). (a) \( f(x, y)=\frac{y}{x} \) (b) \( f(x, y)=\sin \left(\sqrt{x^{2}+y^{2}}\right) \) (c) \( f(x, y)2 answers -
6. Hallar las expresiones indicadas para las funciones dadas. a) \( f(z)=z^{2}+1 ; \quad z=i, i-1,2+3 i \) b) \( g(z)=\frac{1}{z+i} ; \quad z=2-i, 4-2 i, 1+5 i \) c) \( h(z)=\operatorname{Re}\left(z^{2 answers -
2 answers
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5. (12 pts) Solve the I/BVP problem \[ \left\{\begin{array}{l} u_{t}=u_{x x},-\pi \leq x \leq \pi, t \geq 0 \\ u(-\pi, t)=u(\pi, t), u_{x}(-\pi, t)=u_{x}(\pi, t) \\ u(x, 0)=(\sin (x)+2 \cos (x))^{2} \2 answers -
\( \left(e^{x} \operatorname{sen} y-2 y \operatorname{sen}(x)\right) d x+\left(e^{x} \cos y+2 \cos (x)\right) d y=0 \)2 answers -
Prove the following statements. (a) For all \( a, b \in \mathbb{R}, a^{2}+b^{2} \geq 2 a+4 b-5 \). (b) For all \( a, b, c, d \in \mathbb{R},\left(a^{2}+b^{2}\right)\left(c^{2}+d^{2}\right) \geq(a c+b2 answers -
2 answers
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estadistica ayuda por favor
\begin{tabular}{lc} \( \begin{array}{c}\text { 5. Alquitrán (mg) } \\ \text { en cigarrillos } \\ \text { sin filtro }\end{array} \) & Frecuencia \\ \hline \( 10-13 \) & 1 \\ \( 14-17 \) & 0 \\ \( 182 answers -
2 answers
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\( \left\{\begin{array}{l}\frac{(x-4)^{2}}{5}+\frac{(y-1)^{2}}{225}=1 \\ y=2 x+8\end{array}\right. \)2 answers -
2. \( \frac{\sin ^{2} x+\cos ^{2} x}{\tan x}=\cot x \) 3. \( (\cos x)(\sec x-\cos x)=\sin ^{2} x \) 4. \( (\sin x)\left(\csc x+\sin x \sec ^{2} x\right)=\sec ^{2} x \) 5. \( \cos \theta+\sin \theta \t2 answers