Calculus Archive: Questions from June 19, 2023
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20. Resuelva el modelo para un sistema forzado resorte -masa con amortiguamiento \( m \frac{d^{2} x}{d t^{2}}+\beta \frac{d x}{d t}+k x=f(t), x(0)=0, x^{\prime}(0)=0 \), donde la función forzada \( f0 answers -
Find \( y^{\prime}, y^{\prime \prime} \) and \( y^{\prime \prime \prime} \) if \( y=x^{3}-6 x^{2}-5 x+3 \)2 answers -
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Differentiate \( y=2 /\left(2 x^{4}-5\right) \) a. \( y^{\prime}=-16 x^{3} /\left(2 x^{4}-5\right)^{2} \) b. \( y^{\prime}=4 x^{6}+8 x^{3}+4 \) c. \( y^{\prime}=16 x^{3} \) d. \( y^{\prime}=-16 x^{2}2 answers -
8. If \( z=y+f\left(x^{2}-y^{2}\right) \), where \( f \) is differentiable. Find \( y \frac{\partial z}{\partial x}+x \frac{\partial z}{\partial y}=(\quad) \). A. 0 B. \( x \) C. \( y \) D. \( z \)2 answers -
Derive the equation
\( \begin{array}{l}5 .=\frac{x^{4} \sqrt{3 x^{2}-1}}{e^{4 x} \cos x} \\ 7=x^{\cos x} \\ 9 \quad y=(\tan x)^{\ln x} \\ 11 \quad==x^{x^{2}} \\ 13 \quad y=\sin ^{2} x^{x}\end{array} \)2 answers -
Which of the following integral gives the average value of \( f(x, y, z)=6 x y z \) over a domain bounded by \( z=x+y, z=0, y=x, y=0, x=2 \). a. \( \frac{\int_{0}^{2} \int_{0}^{x} \int_{0}^{x+y} d z d2 answers -
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1. Find \( d y / d x \) if \( y=\cos ^{5} x \) a. \( 5 \cos ^{4}(x) \) b. \( -5 \cos ^{4}(x) \sin ^{4}(x) \) c. \( 5 \cos ^{4}(x) \sin (x) \) d. \( -5 \cos ^{4}(x) \sin (x) \) 2. Find \( d y / d x \)2 answers -
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Find dy/dx. Simplify as needed if necessary.
\( x=t+\sin \left(t^{2}+2\right) \) and \( y=\tan \left(t^{2}+3\right) \)0 answers -
5. Given that \( y=x e^{2 x} \), find \( y^{\prime} \) and \( y^{\prime \prime} \), then show that \( y^{\prime \prime}-4 y^{\prime}+4 y=0 \).2 answers -
1. Considere la siguiente función para responder \[ f(x)=\sqrt[3]{x}(x-2) \] a. Halle los valores extremos de \( f \). b. Discuta la concavidad de f. c. Halle los puntos de inflexión de f. d. Trace2 answers -
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Evaluate the double integral. \[ \iint_{D} \frac{y}{x^{2}+1} d A, \quad D=\{(x, y) \mid 0 \leq x \leq 4,0 \leq y \leq \sqrt{x}\} \]2 answers -
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4. Solve the given DE: y" + 25y = 6sin (x) 5. Solve the given DE: y" - 2y' + 2y = extan (x)
4. Solve the given DE: \( y^{\prime \prime}+25 y=6 \sin (x) \) 5. Solve the given DE: \( y^{\prime \prime}-2 y^{\prime}+2 y=e^{x} \tan (x) \)2 answers -
← Evaluate the integral. cos y dy sin 2y + 3 siny - 4 S- cos y dy 2 sin y + 3 siny-4 (Type an exact answer.)
Evaluate the integral. \[ \int \frac{\cos y d y}{\sin ^{2} y+3 \sin y-4} \] \[ \int \frac{\cos y d y}{\sin ^{2} y+3 \sin y-4}= \] (Type an exact answer.)2 answers -
5. Solve the given DE: y" – 2y' + 2y = e*tan (x)
5. Solve the given DE: \( y^{\prime \prime}-2 y^{\prime}+2 y=e^{x} \tan (x) \)2 answers -
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Para la función f(x)=x 3 −75x, su máximo local es: que ocurre en: su mínimo local es: que ocurre en:2 answers
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8. Resuelva la ecuación \( L \frac{d i}{d t}+R i+\frac{1}{C} \int_{0}^{t} i(\tau) d \tau=\mathcal{E}(t) \) sujeta a \( i(0)=0 \mathrm{y} \) (a) \( L=0.1 H, R=3 \Omega, C=0.05 F, \mathcal{E}(t)=100 \m0 answers -
18) If \( y=(\sin x)\left(\cos ^{2} x\right) \). Find \( y^{\prime} \) a) \( 0-2 \sin ^{2} x \cos x+\cos ^{3} x \) b) \( 0-\sin ^{3} x+\cot ^{3} x \) c) \( 2 \sin ^{3} x+\cos ^{2} x \) d) \( 2 \sin ^{2 answers -
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7-12 Find the exact length of the curve. 7. \( x=1+3 t^{2}, \quad y=4+2 t^{3}, \quad 0 \leqslant t \leqslant 1 \) 8. \( y^{2}=4(x+4)^{3}, \quad 0 \leqslant x \leqslant 2, \quad y>0 \) 9. \( x=y^{3 / 22 answers -
james stwart Ex. 11.7 question number 9
5. \( f(x, y)=y^{3}+3 x^{2} y-6 x^{2}-6 y^{2}+2 \) 6. \( f(x, y)=x e^{-2 x^{2}-2 y^{2}} \) 7. \( f(x, y)=x^{3}-12 x y+8 y^{3} \) 8. \( f(x, y)=x y(1-x-y) \) 9. \( f(x, y)=e^{x} \cos y \) 10. \( f(x, y0 answers -
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Find the Jacobian of the transformation. \[ x=2 u / v, \quad y=6 v / w, \quad z=7 w / u \] \[ \frac{\partial(x, y, z)}{\partial(u, v, w)}= \]2 answers -
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\( \begin{array}{l}y=4 \theta^{3} \sin ^{2} \theta \\ x=\frac{\sin t+\cos t}{\sin t-\cos t}\end{array} \)2 answers -
II. ¿Cómo debemos escoger n para que el error sea menor que 0,001 , al aproximar \( \int_{1}^{2} \ln x d x \) utilizando: \( (4 \mathrm{pts}, \mathrm{c} / \mathrm{u}) \) a) La regla de Simpson? b) L2 answers