Advanced Math Archive: Questions from October 30, 2022
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2 answers
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Solve the following initial value problems. 45. \( \left\{\begin{array}{l}y^{\prime \prime}+2 y^{\prime}+y=2 t e^{-2 t}+6 e^{-t}, \\ y(0)=1, \quad y^{\prime}(0)=0 .\end{array}\right. \)2 answers -
2 answers
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2 answers
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Which of the following functions are not linear transformations? From the 5 choices, select all that apply \[ T(x, y, z)=(2 x-3 y, y+z) \] \[ T(x, y)=(1, x-y) \]2 answers -
0 answers
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11. \( y^{\prime \prime}-y^{\prime}+\frac{1}{4} y=3+e^{x / 2} \) 12. \( y^{\prime \prime}-16 y=2 e^{4 x} \) 13. \( y^{\prime \prime}+4 y=3 \sin 2 x \) 14. \( y^{\prime \prime}-4 y=\left(x^{2}-3\right)1 answer -
2 answers
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#5 and #9 only
In Problems \( 1-24 \) solve each differential equation by variation of parameters, State an interval on which the general solution is defined. 1. \( y^{\prime \prime}+y=\sec x \) 2. \( y^{\prime \pri2 answers -
#11 and #21
In Problems 1-24 solve each differential equation by variation of parameters. State an interval on which the general solution is defined. 1. \( y^{\prime \prime}+y=\sec x \) 2. \( y^{\prime \prime}+y=2 answers -
sovle all question
11. \( y^{\prime \prime}-y^{\prime}+\frac{1}{4} y=3+e^{x / 2} \) 12. \( y^{\prime \prime}-16 y=2 e^{4 x} \) 13. \( y^{\prime \prime}+4 y=3 \sin 2 x \)1 answer -
7. \( y^{\prime \prime \prime}+8 y^{\prime \prime}+16 y^{\prime}=0 \) 8. \( y^{\prime \prime}-4 y=24 e^{4 x} \)2 answers -
11. \( y^{\prime \prime}-10 y^{\prime}+25 y=e^{5 x} \) 12. \( y^{\prime \prime}+81 y=36 \sin (9 t)-32 \cos (7 t) \)2 answers -
differential equation
Find a particular solution: - \( y^{\prime \prime}-y^{\prime}+y=e^{x}(2+x) \sin x \) - \( y^{\prime \prime}+3 y^{\prime}-2 y=-e^{2 x}(5 \cos 2 x+9 \sin 2 x) \) - \( y^{4}+4 y=-12 \cos 2 x-4 \sin 2 x \2 answers -
Given \( f(x, y)=-5 x^{3}-2 x^{2} y^{2}-6 y^{4} \), find \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \]2 answers -
18 only
18. \( y^{\prime \prime}+4 y=t^{2}+3 e^{t}, \quad y(0)=0, \quad y^{\prime}(0)=2 \) 19. \( y^{\prime \prime}-2 y^{\prime}+y=t e^{t}+4, \quad y(0)=1, \quad y^{\prime}(0)=1 \)2 answers -
solve using variation of parameters
Solve the IVP \[ y^{\prime \prime}-y^{\prime}-2 y=5 \sin (x), \quad y(0)=1, \quad y^{\prime}(0)=-1 \]2 answers -
Calculate the following contour integrals: Translation:
1.- Calcule \( \oint_{C} \frac{1}{z^{2}} d z \), donde \( C \) es la elipse \( \frac{(x-3)^{2}}{1}+\frac{(y-3)^{2}}{4}=1 \) 2.- Dado el flujo \( f(z)=\overline{\sin z} \), calcule la circulación alre2 answers -
(2 points) Let \( x, y, z \) be (non-zero) vectors and suppose \( w=-4 x-4 y-2 z \). If \( z=-x-y \), then \( w=\quad x+\quad y \). Using the calculation above, mark the statements below that must be2 answers -
2 answers
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0. Discuss the continuity of the function \( f: E^{2} \rightarrow \mathbf{R} \) if (b) \( f(x, y)=\left\{\begin{array}{cc}\frac{x y}{x^{2}+y^{2}} & \text { if }(x, y)=(0,0) \\ 0 & \text { if }(x, y)=(2 answers -
(2 points) Let \( x, y, z \) be (non-zero) vectors and suppose \( w=12 y-9 x+2 z \). If \( z=3 x-4 y \), then \( w= \) Using the calculation above, mark the statements below that must be true. A. \( \2 answers -
need asap
Solve \[ \begin{array}{ll} x^{\prime}=y-x+t & x(0)=6 \\ y^{\prime}=y & y(0)=4 \end{array} \] \( x(t)= \)3 answers -
(2 points) Let \( x, y, z \) be (non-zero) vectors and suppose \( w=4 y-4 x-2 z \). If \( z=y-x \), then \( w=\quad x+\quad y \). Using the calculation above, mark the statements below that must be tr2 answers -
(2 points) Let \( x, y, z \) be (non-zero) vectors and suppose \( w=4 y-4 x-2 z \). If \( z=y-x \), then \( w=\quad x+\quad y \). Using the calculation above, mark the statements below that must be tr2 answers -
Calcule las derivadas parciales de la función \( f(x, y)=\cos \left(x^{2}+y^{2}\right) \) en el punto \( \left(\sqrt{\frac{\pi}{4}}, \sqrt{\frac{\pi}{3}}\right) \), interprete cada uno de los valores2 answers -
Diga si la función \[ f(x, y)=\left\{\begin{array}{ccc} -x^{2}-y^{2} & \text { si } & x y \neq 0 \\ 1 & \text { si } & x y=0 \end{array}\right. \] es diferenciable en \( (0,0) \).2 answers -
Sea \( A \subset \mathbb{R}^{n} \), un punto \( x \in A \) se define como punto de acumulación si, para cualquier \( \varepsilon>0 \) se cumple \( \mathcal{B}_{x}(\varepsilon) \cap(A \backslash\{x\})2 answers -
Calculate the limits if they exist
Calcule los siguientes límites, si es que existen: (a) \( \lim _{(x, y) \rightarrow(1,0)} \frac{x^{2}-y}{y-x y} \) (b) \( \lim _{(x, y) \rightarrow(0,0)} \frac{1-\cos \left(x^{2}+y^{2}\right)}{x^{2}+2 answers