Calculus Archive: Questions from January 30, 2023
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PLEASE COMPLETE THE QUESTION WITH CLEAR EXPLANATION
Q38: If \( y=e^{2 x} \sin 5 x \), then which of the following is true? (a) \( y^{\prime \prime}-4 y^{\prime}+30 y=0 \) (b) \( y^{\prime \prime}-4 y^{\prime}+30 y=1 \) (c) \( y^{\prime \prime}-4 y^{\pr2 answers -
1. Find \( \frac{\partial r}{\partial u}, \frac{\partial r}{\partial v} \) and \( \frac{\partial r}{\partial t} \) for \( r=x \ln y, x=3 u+v t, y=u v t \).2 answers -
\( \int \cos ^{3}\left(\frac{t}{2}\right) \sin ^{2}\left(\frac{t}{2}\right) d t= \) \( \int \tan ^{4} x \sec ^{6} x d x= \) \( \int \tan x \sec ^{4} x= \) \( \int \sin 5 x \cos ^{4} 4 x d x= \)2 answers -
Find \( \mathbf{a}+\mathbf{b}, 9 \mathbf{a}+3 \mathbf{b},|\mathbf{a}| \), and \( |\mathbf{a}-\mathbf{b}| \) \[ \mathbf{a}=8 \mathbf{I}-4 \mathbf{j}+3 \mathbf{k}, \quad \mathbf{b}=5 \mathbf{l}-9 \mathb2 answers -
Hallar el área de la región que queda fuera de:
\( r=1+\cos \theta \quad y \) dentro de \( r=3 \cos \theta \) a. Dibujar la región utilizar el graficador de funciones Wplotsp. (4 pts.) b. Determinar límites de integración. (2 pts.) c. Evaluar l2 answers -
For questions 7 and 8 , find the extrema of 7. \( f(x, y)=x^{4}+y^{3}+32 x-9 y \). 8. \( f(x, y)=e^{x} \sin y \).2 answers -
Problema: Discuta como usted determina la transformada de Laplace de la siguiente función: \[ f(t)=\left\{\begin{array}{c} 2,0 \leq t2 answers -
Need help finding the lateral limit when x approaches to 3 from the right
\[ f(x)=\left\{\begin{array}{lcc} x^{2}+x-4 & \text { si } & x \leq-2 \\ x+1 & \text { si } & -22 answers -
d the derivative of \( y=\sqrt{11 x^{3}-8 x^{2}-\frac{8}{x}} \) \[ \begin{aligned} y^{\prime} & =\frac{1}{2 \sqrt{33 x^{2}-16 x+\frac{8}{x^{2}}}} \\ y^{\prime} & =\frac{11 x^{4}-8 x^{3}-8}{2 \sqrt{332 answers -
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Evalúe el integral cambiando a coordenadas polares a) \( \int_{-1}^{1} \int_{0}^{\sqrt{1-x^{2}}} \cos \left(x^{2}+y^{2}\right) d y d x \) b) \( \int_{0}^{3} \int_{0}^{\sqrt{9-x^{2}}}\left(x^{2}+y^{2}2 answers -
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7) On a separate paper, sketch the following plots: i. \( y=\frac{1}{x} \) ii. \( y=\frac{1}{x^{2}} \) iii. \( \quad y=e^{x} \) iv. \( y=e^{-x} \) v. \( y=\ln x \) vi. \( y=\ln e^{x} \) vii. \( y=(x-32 answers -
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\( y=x^{4}-2 x^{2}+6 \) \( (x, y)=(\quad) \quad \) (smallest \( x \)-value) \( (x, y)=( \) \( (x, y)=(\quad \) (largest \( x \)-value)0 answers