Calculus Archive: Questions from October 18, 2023
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Ferentiate \( y=e^{8 x \cos (8 x)} \). \[ \frac{d y}{d x}=[8 \cos (8 x)+8 x \cdot 8 \sin (8 x)] \cdot e^{8 x \cos (8 x)} \]1 answer -
solve correctly plz
3. SOLVE THE FOLOWING IVP \[ \begin{aligned} (1+\cos x) y^{\prime} & =\left(1+e^{-y}\right) \sin x \\ y(0) & =0 \end{aligned} \]1 answer -
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1. For the following exercise, find \( y^{\prime} \), the derivative of \( y \) with respect to \( x \), for the given function. (a) \( y=x^{2} e^{2 x} \) (b) \( y=\sqrt{e^{2 x}+2 x} \) (c) \( y=2^{x}1 answer -
Q 2. (2 marks) Find \( \frac{d y}{d x} \) in the follwoing (a) \[ y=\frac{\left(x^{2}-5\right)^{3}}{\sqrt{x^{2}+2}} \] (b) \[ y=\sin ^{2}(2 x+y) \text {. } \]1 answer -
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Solve. 2x 7 11 15 -³ ([ ²8 -2²] + [ 2², ²)) = [ ¹5 -2²7] -3 6 -7 -y 3 12 (x, y) = ( [
Solve. \[ -3\left(\left[\begin{array}{cc} 2 x & -2 \\ 6 & 1 \end{array}\right]+\left[\begin{array}{cc} 7 & 11 \\ -7 & -y \end{array}\right]\right)=\left[\begin{array}{cc} 15 & -27 \\ 3 & 12 \end{array1 answer -
Transcripción: integral de (e^(z^2 - 2^z))/(z+2-3i)^2
Ejeracios: \[ e_{1} \text { en }|E| \equiv 2 \] \( c_{2} \) en \( c_{1}(2+2 i) C^{\prime} \) en \( c_{2}(1-2 i) \).0 answers -
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Evaluate \( \iiint_{\mathcal{B}} f(x, y, z) d V \) for the specified function \( f \) and box \( \mathcal{B} \). \[ f(x, y, z)=\frac{z}{x} ; \quad 1 \leq x \leq 3, \quad 0 \leq y \leq 2, \quad 0 \leq1 answer -
Find \( \frac{\partial f}{\partial u} \) and \( \frac{\partial f}{\partial v} \) if \( f(x, y)=3 x+y \sin x, x(u, v)=u^{2}+v^{2} \), and \( y(u, v)=u v \).1 answer -
urgent pls help
a) \( f(x)=-3 x^{5}+7 x^{3}-8 x \) b) \( g(x)=\frac{5 x}{7}-\frac{2}{x} \) c) \( y=2 \sqrt{t}+\sqrt[3]{t} \) d) \( f(\theta)=2 \sin \theta-\cos \theta \) e) \( f(x)=-2 x^{3} e^{x} \) f) \( y=\frac{x^{1 answer -
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Ejercicio 1. Calcule la derivada de las siguientes funciones y simplifque su respuesta. (a) \( f(x)=\frac{4 x^{2}}{3}-\frac{2}{3 x^{2}} \) (d) \( f(x)=\frac{2 x^{2}+4 x+1}{3 x-1} \) (g) \( f(x)=(3-2 x1 answer -
Ejercicio 2. Determine si es posible aplicar la regla de L'Hôpital para evaluar los siguientes límites. Si es posible, utilícelo para calcular el límite dado. Si no es posible aplicar L'Hôpital,1 answer -
\[ C(x)=400,000+160 x+0.001 x^{2} \] (a) Encuentre la función de costo marginal y úsela para estimar qué tan rápido el costo está aumentando cuando \( x=10,000 \). Compárelo con el valor exacto1 answer -
Ejercicio 4. Las ventas mensuales del nuevo sistema de sonido de Sunny Electronics están dadas por la función \( q(t)=2,000 t-100 t^{2} \) unidades por mes. El precio (en dólares) por cada sistema1 answer -
Ejercicio 5. El valor promedio de las casas (en miles de dólares) en los Estados Unidos durante el periodo de Enero-2010 a Enero-2015 se puede aproximar con la función: \[ P(t)=4.5(t-2010)^{2}-15(t-1 answer -
Find \( y^{\prime \prime} \) for \( y=-6\left(x^{2}+5\right)^{3} \) \[ y^{\prime \prime}=-36\left(x^{2}+5\right)\left(5 x^{2}+5\right) \]1 answer -
Considerando el siguiente campo vectorial: \[ F(x, y)=\left(x^{2}+y^{2}\right) \mathbf{i}+2 x y \mathbf{j} \] a) Argumentar detalladamente si es un campo vectorial conservativo (10 puntos). b) Encontr1 answer -
(1 point) Find ff f(x, y) dA where f(x, y) = 3x + 5 and R = [2, 5] × [-2, 1]. SR f(x, y) dA = 63/2
(1 point) Find \( \iint_{R} f(x, y) d A \) where \( f(x, y)=3 x+5 \) and \( R=[2,5] \times[-2,1] \). \[ \iint_{R} f(x, y) d A= \]1 answer -
\( \begin{array}{l}\text { Find } \frac{d y}{d x} \\ \qquad \begin{array}{l}y=3 x^{3}\end{array}\end{array} \) \( \frac{d y}{d x}= \)1 answer -
find dy/dx
\( y=1+\sin ^{2}(3 x)+\sin ^{4}(3 x)+\sin ^{6}(3 x)+\sin ^{8}(3 x)+\ldots+\sin ^{2024}(3 x) \).2 answers -
explica paso a paso la integral
\( \begin{array}{l}-(x-2)^{2}+4 \\ \text { - } \int \frac{d x}{\sqrt{4-(x-2}} \quad u=x-2 \quad a^{2}=4, a=2 \\ \int \frac{d u}{\sqrt{a^{2}-u^{2}}}=\operatorname{sen}^{-1}\left(\frac{u}{a}\right)+c \\1 answer -
explica paso a paso la integral
\( \begin{array}{l}\text { v) } \int \frac{d x}{\sqrt{x}(x+1)\left[\left(\tan ^{-1} \sqrt{x}\right)^{2}+9\right.} \\ u=\tan ^{-1} \sqrt{x}, a^{2}=9, a=3 \\ d u=\frac{1}{1+x} \frac{d}{d x} \sqrt{x}=\fr1 answer -
7. Given \( z=f(x, y)=2 x^{2}-x y+y^{2} \), find (i) \( f_{x}(x, y) \) (ii) \( f_{x}(1,-1) \) (iii) \( f_{y}(x, y) \) (iv) \( f_{y}(1,-1) \) (v) the linear approximation \( L(x, y) \) at \( (1,-1) \)1 answer -
2. Find \( y^{\prime} \) and \( y^{\prime \prime} \). (a) \( y=(1+\sqrt{x})^{3} \) (b) \( y=e^{e^{x}} \)1 answer -
f(x) = 8(5x² + 4)5 {| (g(x), h(x)} = f'(x) = I
\( \begin{array}{l}f(x)=8\left(5 x^{2}+4\right)^{5} \\ h(x)\}=\{ \\ f^{\prime}(x)=\end{array} \)1 answer -
(1 point) Find the gradient of \( f(x, y)=x\left(6 x^{2}+7 y^{2}\right)^{\frac{8}{3}} \). \[ \nabla f(x, y)= \]1 answer -
2 (1 point) Find the gradient of f(x, y) = cos (6x² - 9y²). Vf(x, y) =
(1 point) Find the gradient of \( f(x, y)=\cos \left(6 x^{2}-9 y^{2}\right) \) \( \nabla f(x, y)= \)1 answer -
Problem 1: Given the following functions: \[ \begin{aligned} f(x, y) & =x^{2} y^{3}+e^{x y}+\ln \left(x y^{2}\right) \\ g(x, y, z) & =\cos \left(x y z^{2}\right)+\sin (y z)+x y z+e^{x+y z} \end{aligne1 answer -
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(1 point) Find the Jacobi matrix for \( \vec{f}(x, y)=\left[\begin{array}{c}x-6 y \\ 3 x^{6}\end{array}\right] \) \[ (D \vec{f})(x, y)= \]1 answer -
(1 point) Find the Jacobi matrix for \( \vec{f}(x, y)=\left[\begin{array}{c}(2 x+7 y)^{2} \\ \sin (3 x+2 y)\end{array}\right] \) \[ (D \vec{f})(x, y)= \]1 answer -
(1 point) Find the Jacobi matrix for \( \vec{f}(x, y)=\left[\begin{array}{c}\ln \left(6 x^{2}+7 y^{2}\right) \\ e^{7 x+4 y}\end{array}\right] \) \( (D \vec{f})(x, y)= \)1 answer -
Find all values of \( x \) and \( y \) such that \( f_{x}(x, y)=0 \) and \( f_{y}(x, y)=0 \) simultaneously. \[ \begin{array}{l} f(x, y)=x^{2}+3 x y+y^{2}-13 x-12 y+35 \\ (x, y)=(\quad) \\ \end{array}1 answer -
all odd problems
Find the derivative of the functions in Problems 1-27. 1. \( f(x)=(x+1)^{99} \) 2. \( g(x)=\left(4 x^{2}+1\right)^{7} \) 3. \( w=\left(t^{2}+1\right)^{100} \) 4. \( R=\left(q^{2}+1\right)^{4} \) 5. \(1 answer -
Find y'. 1 y = tan (2x + 1) 4
Find \( \mathrm{y}^{\prime \prime} \). \[ y=\frac{1}{4} \tan (2 x+1) \]1 answer -
Un termómetro se cambia de una habitación, cuya temperatura es de \( 15.3^{\circ} \mathrm{C} \), al exterior donde la temperatura del aire es de \( -8^{\circ} \mathrm{C} \). Después de transcurrido1 answer -
1. Hallar \( d y / d x \) sabiendo que \[ 2 x^{3}+x^{2} y-x y^{3}=2 \] 2. Hallar \( d y / d x \) sabiendo que \[ x^{2} y^{2}+x \operatorname{sen} y=4 \] 3. Hallar \( \mathrm{dy} / \mathrm{dx} \) sabie1 answer -
Find \( \iint_{R} f(x, y) d A \) where \( f(x, y)=x \) and \( R=[1,6] \times[0,5] \). \( \iint_{R} f(x, y) d A= \)1 answer -
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Find a particular solution to \[ y^{\prime \prime}-2 y^{\prime}+y=\frac{-15 e^{t}}{t^{2}+1} \] \[ y_{p}= \]1 answer -
Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-13 y^{\prime \prime}+40 y^{\prime}=28 e^{x} \text {, } \] \[ \begin{array}{l} y(0)=28, y^{\prime}(0)=13, y^{\prime \prime}(0)=29 \\1 answer -
1.) Solve the homogenous I.V.P d.) y ₁ - 2y² + 2y = 0, Y (7) = e ²₁ y ² (T) = 0 b.) y - 4y " + 7y - 6y = 0, y(0) = 1, y '(0) = 0, y "(0) =0
Solve the homogenous I.V.P d. \( y^{\prime \prime}-2 y^{\prime}+2 y=0, \quad y(\pi)=e^{\pi}, \quad y^{\prime}(\pi)=0 \) b.) \( y^{\prime \prime \prime}-4 y^{\prime \prime}+7 y^{\prime}-6 y=0, y(0)=1,1 answer -
1. Hallar \( \mathrm{dy} / \mathrm{dx} \) sabiendo que \[ 2 x^{3}+x^{2} y-x y^{3}=2 \] 2. Hallar dy/dx sabiendo que \[ x^{2} y^{2}+x \operatorname{sen} y=4 \]1 answer -
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odd problems
For Problems 3-32, find the derivative. Assume that \( a, b, c \), and \( k \) are constants. 3. \( f(t)=t e^{-2 t} \) 4. \( f(x)=x e^{x} \) 5. \( y=t^{2}(3 t+1)^{3} \) 6. \( y=5 x e^{x^{2}} \) 7. \(1 answer -
4. Hallar \( d y / d x \) sabiendo que \[ x^{2}+y^{3}-2 y=3 \] A continuación, calcular la pendiente y la recta tangente en el punto \( (2,1) \). Haga la gráfica correspondiente.1 answer -
contestar la integral triple en coordenadas cilindricas
22. Encuentre el volumen del sólido que está dentro del cilindro \( x^{2}+y^{2}=1 \) y la esfera \( x^{2}+y^{2}+z^{2}=4 \).1 answer -
Find the limit. \[ \lim _{p \rightarrow(8,8,0)}\left(\sin ^{2} x+\cos ^{2} y+4 \sec ^{2} x\right) \]1 answer -
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Find all the second partial derivatives. \[ f(x, y)=\ln (a x+b y) \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y)= \]1 answer -
Evaluate f(x, y, z) dv for the specified function f and box B. Z f(x, y, z) = — ; 1 ≤x≤ 7, 0 ≤ y ≤ 4, X 0AZN2
Evaluate \( \iiint_{\mathcal{B}} f(x, y, z) d V \) for the specified function \( f \) and box \( \mathcal{B} \). \[ f(x, y, z)=\frac{z}{x} ; \quad 1 \leq x \leq 7, \quad 0 \leq y \leq 4, \quad 0 \leq1 answer -
Find the derivative. y' || 8 7 √t t² y = 7t² + 70² + -
Find the derivative. \[ y=7 t^{2}+\frac{8}{\sqrt{t}}-\frac{7}{t^{2}} \] \[ y^{\prime}= \]1 answer -
If \( \vec{r}(t)=(a \cos t, a \sin t), t \in[0,2 \pi] \), and \( \vec{F}(x, y)=(-y, x) \). Evaluate \( \int_{C} \vec{F} \cdot d \vec{r} \).1 answer -
11 and 13 please.
9-24 Find the exact length of the curve. 9. \( y=\frac{2}{3} x^{3 / 2}, \quad 0 \leqslant x \leqslant 2 \) 10. \( y=(x+4)^{3 / 2}, \quad 0 \leqslant x \leqslant 4 \) 11. \( y=\frac{2}{3}\left(1+x^{2}\1 answer -
Solve the given initial-value problem. \[ y^{\prime \prime}+x(y)^{2}=0, y(1)=3, y^{\prime}(1)=2 \] \[ y= \]1 answer -
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(1 point) Calculate all four second-order partial derivatives of \( f(x, y)=3 x^{2} y+3 x y^{3} \). \[ \begin{array}{l} f_{x x}(x, y) \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \\ f_{y y}(x, y)= \end{array}1 answer -
\( (10 \mathrm{pts}) \) Let \( f(x, y)=x^{2} \sec (y) \). Find \( f_{x y}\left(\sqrt{2}, \frac{\pi}{4}\right) \).1 answer -
Use implicit differentiation to find \( y^{\prime} \). Then evaluate \( y^{\prime} \) at \( (2,6) \). \[ 5 x^{3}-y^{2}-4=0 \] \[ \begin{array}{l} y^{\prime}= \\ \left.y^{\prime}\right|_{(2,6)}= \\ y^{1 answer -
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integral con coordenadas cilindricas
Calcula el volumen delimitado por los paraboloides \( z=x^{2}+y^{2} \) y \( z=2-x^{2}-y^{2} \).1 answer -
2. Calcula la Integral siguiente: \( 2 \cdot \int_{0}^{2 \pi} \int_{R_{2}}^{R_{1}} \int_{0}^{\sqrt{R_{1}^{2}-r^{2}}} r \cdot d z \cdot d r \cdot d \theta \)1 answer -
number 13 please
11-18 Find the differential of the function. 11. \( y=e^{5 x} \) 12. \( y=\sqrt{1-t^{4}} \) 13. \( y=\frac{1+2 u}{1+3 u} \) 14. \( y=\theta^{2} \sin 2 \theta \) 15. \( y=\frac{1}{x^{2}-3 x} \) 16. \(1 answer -
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number 17 please
11-18 Find the differential of the function. 11. \( y=e^{5 x} \) 12. \( y=\sqrt{1-t^{4}} \) 13. \( y=\frac{1+2 u}{1+3 u} \) 14. \( y=\theta^{2} \sin 2 \theta \) 15. \( y=\frac{1}{x^{2}-3 x} \) 16. \(1 answer -
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Determine el volumen de la región acotada por arriba por el plano \[ f(x, y)=4 x+18 \] y abajo por la región encerrada por las curvas \[ y=4-x^{2} \quad \& \quad y=3 x \] en el plano \( x y \).1 answer -
El área de la siguiente región se calcula mediante la integral doble \[ A=\int_{0}^{8} \int_{-x}^{3 \sqrt[3]{x}} d y d x \] Intercambie el orden de integración para obtener la misma área.1 answer