Advanced Math Archive: Questions from June 12, 2023
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Solve the following initial value problem: \[ \mathrm{y}^{\prime \prime}+\mathrm{y}=4 \delta(\mathrm{t}-2 \pi), \mathrm{y}(0)=1, \mathrm{y}^{\prime}(0)=0 \]2 answers -
\[ \int_{-4}^{1-e} \int_{1-x}^{5} f(x, y) d y d x+\int_{1-e}^{1} \int_{e}^{5} f(x, y) d y d x+\int_{1}^{\ln 5} \int_{e^{x}}^{5} f(x, y) d y d x=? \] \( \left.A) \int_{e}^{4} \int_{1-y}^{\ln y} f(x, y)2 answers -
\[ \int_{-2}^{1-e} \int_{1-x}^{3} f(x, y) d y d x+\int_{1-e}^{1} \int_{e}^{3} f(x, y) d y d x+\int_{1}^{\ln 3} \int_{e^{x}}^{3} f(x, y) d y d x=? \] \[ \int_{e}^{4} \int_{1-y}^{\ln y} f(x, y) d x d y2 answers -
Ins 5 f(x,y) dydx + [ [ f(x,y)dydx + [ [ f(x,y)dydx =? 1-e e Iny 1-e 5 [ frax -4 1-x 15 5 ln y 4) f(x,y) dxdy B) f(x,y)dxdy C) e 1-y e 1-y jjra. e 1+y ] b][rodudy D) jj, f(x,y)dxdy -3 1+y f(x, y)dxdy
\[ \int_{-4}^{1-e} \int_{1-x}^{5} f(x, y) d y d x+\int_{1-e}^{1} \int_{e}^{5} f(x, y) d y d x+\int_{1}^{\ln 5} \int_{e^{x}}^{5} f(x, y) d y d x=? \] A) \( \int_{e}^{1} \int_{x-y}^{\tan y} f(x, y) d x2 answers -
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function is regular m=?
\( f(x, y)=\left\{\begin{array}{cc}\frac{2 x y-2 x-4 y+4}{2-2 y}, & (x, y) \neq(1,1) \\ m, & (x, y)=(1,1)\end{array}\right. \)2 answers -
largest domain=?
\( f(x, y)=\frac{1}{\sqrt{4-x^{2}-y^{2}}}-\ln (x+y) \) fonksiyon \[ \begin{array}{l} D=\left\{(x, y): x^{2}+y^{2}2 answers -
Solve the initial value problem \[ y^{\prime \prime}+9 y=-18 \sin (3 x), \quad y(0)=\frac{19}{10}, \quad y^{\prime}(0)=6 \]2 answers -
Evaluate the integral \[ \int_{0}^{1} \int_{0}^{z} \int_{0}^{1+2+y} f(x, y, z) d z d y d x \] where \( f(x, y, z)=1 \).2 answers -
please assist
\( \lim _{(x, y, z) \rightarrow(0,0,0)} f(x, y, z)=\lim _{(x, y, z) \rightarrow(0,0,0)} \frac{x y+y z^{2}+x z^{2}}{x^{2}+y^{2}+z^{2}}= \)2 answers -
Solve the following optimization exercise with constraints: You currently work in a company dedicated to the production of controllers for electric door lifts of a certain model of car. Your job as a
Actualmente laboras en una empresa dedicada a la producción de controladores para elevadores eléctricos de las puertas de un determinado modelo de auto. Tu labor como representante del área de vent2 answers -
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x = √9-6² y = Sin' ( 2 ) find dy/de ldx
\[ \begin{array}{l} x=\sqrt{9-t^{2}} \\ y=\sin ^{-1}\left(\frac{t}{3}\right) \end{array} \] find \( d y / d x \)2 answers -
buscar la tabla de valores, dominio y campo de valores
1. Si \( f(x)=3^{x} \); hallar: a. \( v(x)=f(x)-1 \); traza su grafica e indica su Dominio y Campo de Valores2 answers -
1. Si \( f(x)=3^{x} \); hallar: a. \( v(x)=f(x)-1 \); traza su grafica e indica su Dominio y Campo de Valores b. Una fórmula para \( v^{-1}(x) \), traza su grafica e indique su Dominio y Campo de Va2 answers -
4. \( f(x, y, z)=x y+x z+y z, g(x, y, z)=y+z^{2} \) Find extrema of \( f(x, y, z) \) such that \( g(x, y, z)=1 \).2 answers -
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Multivariable Calculus
2. \( f(x, y, z)=\ln \left(x^{2}+y z\right), g(x, y, z)=e^{x^{2}+y z}, P(1,1,1) \) Find \( D_{\hat{v}} f(x, y, z), D_{\hat{w}} g(x, y, z) \), where \( \vec{v}=\nabla g(P), \vec{w}=\nabla f(P) \)2 answers -
Convecto! Si: A B C D D Resuelva para X la siguiente ecuación: [1] -7 16 9 A = - 3 -23 144 −4 25 29 5 B = C = 7-8 -7 [47] -1 2 AXC-B-0. ¿como se soluciona?
\[ \begin{array}{l} A=\left[\begin{array}{ll} 6 & -7 \\ 1 & -1 \end{array}\right] \\ \mathbf{B}=\left[\begin{array}{rr} 7 & -8 \\ 1 & -1 \end{array}\right] \\ C=\left[\begin{array}{rr} 4 & -7 \\ -1 &2 answers -
(1) Calcule el rotacional y divergencia de los siguientes campos vectoriales (a) \( x y^{2} z^{2} \vec{i}+x^{2} y z^{2} \vec{j}+x^{2} y^{2} z \vec{k} c \) (b) \( x y e^{z} \vec{i}+y z e^{x} \vec{k} \)0 answers -
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