Advanced Math Archive: Questions from December 10, 2022
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2 answers
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Q6 & Q8
Solve the ODE by integration differentiation formula. 1. \( y^{\prime}+2 \sin 2 \pi x=0 \) 2. \( y^{\prime}+x e^{-x^{2} / 2}=0 \) 3. \( y^{\prime}=y \) 4. \( y^{\prime}=-1.5 y \) 5. \( y^{\prime}=4 e^2 answers -
2.4 Solve the initial value problem \[ \begin{array}{c} y^{\prime \prime}+2 y^{\prime}+y=0 \\ y(0)=2, \quad y^{\prime}(0)=-1 \end{array} \]2 answers -
4 Solve the initial value problem \[ \begin{array}{c} y^{\prime \prime}+2 y^{\prime}+y=0 \\ y(0)=2, \quad y^{\prime}(0)=-1 \end{array} \]2 answers -
5). If \( f^{\prime}(3)=2 \), then \( \lim _{h \rightarrow 0} \frac{f(3-h)-f(3)}{2 h}= \) (A) 1 (B) 0 (C) 2 (D) \( -1 \)2 answers -
(12). The total differential of \( z=x y+\frac{x}{y} \) is (A) \( d z=\left(y+\frac{1}{y}\right) d x+\left(x-\frac{x}{y^{2}}\right) d y \). (B) \( d z=\left(x-\frac{x}{y^{2}}\right) d x+\left(y+\frac{2 answers -
Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For Part of the surface \( x=z^{3} \), where \( 0 \leq x, y \leq 14^{-\frac{3}{2}} ; \quad f(x, y, z)=x \) \( \iint_{\mathcal{S}} f(x, y, z) d S= \)2 answers -
3.) \( y=\frac{\sin x}{\cos ^{2} x}+\ln \left(\frac{1+\sin x}{\cos x}\right) \) ise \( y^{\prime}= \) ?2 answers -
Given the following partially filled table for \( y=2 x^{2} \) : Determine \( \left.\lim _{\Delta x \rightarrow 0} \frac{\Delta y}{\Delta x}\right|_{[2, x]} \)2 answers -
(1 point) Solve the initial value problem \[ y^{\prime \prime}+3 x y^{\prime}-12 y=0, y(0)=9, y^{\prime}(0)=0 \] \[ y= \]2 answers -
#6 please
In Exercises 1-17 find a particular solution. 1. \( y^{\prime \prime}+3 y^{\prime}+2 y=7 \cos x-\sin x \) 2. \( y^{\prime \prime}+3 y^{\prime}+y=(2-6 x) \cos x-9 \sin x \) 3. \( y^{\prime \prime}+2 y^2 answers -
IFind and draw the domain of the Find and draw the domain of the function
Halla y dibuja el dominio de la función \[ f(x, y)=\sqrt{x-1}+\sqrt{y-2}+\sqrt{3-x}+\sqrt{4-y} \]2 answers -
Assume that z satisfies the equation z! + xy - y" = 3. Assume that this defines z as a function of x and y, determine #$ + #$ at the point (x,y,z) = (1,2,3).
\( \left[6\right. \) pts.] Suponer que \( z \) satisface la ecuación \( z^{2}+x y-y^{3}=3 \). Asumir que esto define \( z \) como función de \( x \) y de \( y \), determina \( \frac{\partial z}{\par2 answers -
Find the maximum and minimum values and saddle points of the function
Halla los valores máximos y mínimos, y los puntos de silla de la función \[ f(x, y)=x y+\frac{1}{x}+\frac{1}{y} \]2 answers -
Evaluate the integral J' J' cos(y!) dy dx by changing the order of integration.
Evalúa la integral \( \int_{0}^{1} \int_{x}^{1} \cos \left(y^{2}\right) d y d x \) cambiando el orden de integración.2 answers -
Calculate the / [ / / × dV where R is the tetrahedral region bounded by the planes ) x = 0; y = 0, z = 0 and x + y + z. = 2.
[6 pts.] Calcula la \( \iiint_{R} x d V \) donde \( R \) es la región tetrahedral acotada por los planos \( x=0, y=0, z=0 \) y \( x+y+z=2 \).2 answers -
2 answers
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The temperature of a region in space is given by T(x, y, z) =. x!yz." Find the rate of maximum growth at (2, 1, -1) and find the unit vector in that direction.
[7 pts.] La temperatura de una región en el espacio está dada por \( T(x, y, z)= \) \( x^{2} y z^{3} \). Halla la tasa de máximo crecimientos en \( (2,1,-1) \) y halla el vector unitario en esa dir2 answers -
Let C be the curve given by r(t) = (t! + 1, 3*) for 0 st s 1. Consider the vector field F(x, y) = (y, x) . Show that F(x, y) is a conservative vector field, and then computes / F(x, y) • dr.
[6 pts.] Sea \( C \) la curva dada por \( r(t)=\left\langle t^{2}+1,3^{t}\right\rangle \) para \( 0 \leq t \leq .1 \). Considera el campo vectorial \( F(x, y)=\langle y, x\rangle \). Muestra que \( F(2 answers -
2 answers
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Problem \( 2(4 \mathrm{pts}) \). Compute \( d \omega \) if a) \( \omega=(4 x y) d x+y^{2} d y \); b) \( \omega=(x+y+z) d x \wedge d y+\left(y^{2} x\right) d y \wedge d z+(x y z) d z \wedge d x \).2 answers -
Find \( (3) B A+(4) A C \), if possible. \[ A=\left[\begin{array}{rrr} 0 & 1 & -1 \\ 0 & -1 & 0 \end{array}\right] \quad B=\left[\begin{array}{rr} 1 & 1 \\ -1 & 1 \end{array}\right] \quad C=\left[\beg2 answers -
2 answers
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6. If possible diagonalize \( A \) \[ A=\left[\begin{array}{rrr} -3 & -2 & 0 \\ 14 & 7 & -1 \\ -6 & -3 & 1 \end{array}\right] \]2 answers -
Vectorial camp F and solid (appears above). Verify Theorem of divergence in this case
6. Sea el campo vectorial \[ F=\langle-y, x, z\rangle \] y el sólido \[ \left\{(x, y, z): x^{2}+y^{2} \leq 1 ;-2 \leq z \leq 3\right\} . \] Verificar el Teorema de la divergencia en este caso.2 answers -
Solve the initial value problem \( y^{\prime \prime}+y^{\prime}-6 y=t e^{2 t} ; y(0)=1, y^{\prime}(0)=-2 \).2 answers