Calculus Archive: Questions from February 19, 2023
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Differentiate the function. I need help with questions 13,15,17,19, 21, and 23.
13. \( A(s)=-\frac{12}{s^{5}} \) 14. \( B(y)=c y^{-6} \) 15. \( g(t)=2 t^{-3 / 4} \) 16. \( h(t)=\sqrt[4]{t}-4 e^{t} \) 17. \( y=3 e^{x}+\frac{4}{\sqrt[3]{x}} \) 18. \( y=\sqrt{x}(x-1) \) 19. \( F(x)=2 answers -
consider the function: a. Find the tangent plane to the surface at the point (3, 1, 1) b. Find the normal line to the surface at (3,1,1)
3. Consideremos la función: \[ f(x, y)=\frac{1}{6}\left(e^{y-1} x^{2}-3 y^{2}\right)=z \] a. Encontrar el plano tangente a la superficie en el punto \( (3,1,1) \) b. Encontrar la recta normal a la su1 answer -
5. Let f(x, y) = x³+4x²y-2y and u=(1/3,2sqrt(2)/3) Find the gradient of f. (ii) Find the directional derivative Du f(x, y) at (-1,2) (iii) Find the direction of the greatest directional derivative o
5. Sea \( f(x, y)=x^{3}+4 x^{2} y-2 y \quad \) y \( \quad u=\langle 1 / 3,2 \sqrt{2} / 3\rangle \). (i) Encontrar el gradiente de \( f \). (ii) Encontrar la derivada direccional \( D_{\mathrm{u}} f(x,2 answers -
6. Let F(x, y, z) = x³+4x²y - 2y - z a) What are the level surfaces of F? b) Give the gradient of F. c) VF(-1,2,1)
6. Sea \( F(x, y, z)=x^{3}+4 x^{2} y-2 y-z \) a) ¿C Cuales son las superficies de nivel de \( F \) ? b) Dar el gradiente de \( F \). c) \( \nabla F(-1,2,1) \)2 answers -
31-33 Use Formula 11 to find the curvature. 31. \( y=x^{4} \) 32. \( y=\tan x \) 33. \( y=x e^{x} \)2 answers -
Find \( y^{\prime} \) and \( y^{\prime \prime} \) by implicit differentiation. \[ \begin{array}{l} 4 x^{3}-5 y^{3}=3 \\ y^{\prime}= \\ y^{\prime \prime}= \end{array} \]2 answers -
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Find each limit. \[ f(x, y)=3 x^{2}+4 y^{2} \] (a) \( \lim _{\Delta x \rightarrow 0} \frac{f(x+\Delta x, y)-f(x, y)}{\Delta x} \) (b) \( \quad \lim _{\Delta y \rightarrow 0} \frac{f(x, y+\Delta y)-f(x2 answers -
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ODE
\( \begin{array}{l}y d x+\left(2 x y-e^{-2 y}\right) d y=0 \\ (2 x+y+1) \frac{d y}{\partial x}=1 \\ \frac{\partial y}{d x}=(x+y+4)^{2}\end{array} \)2 answers -
La ecuación de estado de Dieterici está dada por: \[ P e^{\frac{a}{V_{m}} R}=\frac{D T}{V_{m}-E} \] donde \( a, b \) y \( R \) son constantes. Caleule: a) \( \left(\frac{\partial V_{m}}{\partial P}\2 answers -
La ecuación de estado de Soave-Redlich-Kwong está dada por: \[ P=\frac{R T}{V_{m}-b}-\frac{a}{V_{m}\left(V_{m}+b\right)} \] donde \( a, b \) y \( R \) son constantes. Caclule: a) \( \left(\frac{\par0 answers -
Find \( y^{\prime} \) if \( y=\ln \left(9 x^{2}+5 y^{2}\right) \). \[ y^{\prime}=\frac{18 x}{9 x^{2}+5 y^{2}} \] Find \( y^{\prime} \) if \( x^{y}=y^{x} \).2 answers -
please answer both! please answer both!
Solve the differential equation \( \frac{d y}{d x}=\frac{x^{3}}{y^{2}} \). A. \( y=\sqrt[3]{\frac{3 x^{4}}{4}+C} \) B. \( y=\sqrt[3]{\frac{4 x^{4}}{3}+C} \) C. \( y=\sqrt[3]{\frac{3 x^{4}}{4}}+C \) D.2 answers -
Differentiate the function. \[ \begin{array}{c} y=\log _{7}\left(e^{-x} \cos (\pi x)\right) \\ y^{\prime}=\frac{\log _{7}\left(e^{-x} \cos (\pi x)\right)\left(\log _{7}(e) \ln (7)+\pi \tan (\pi x)\rig2 answers -
Differentiate the function. Need help with Q. 25,27,29,31.
13. \( A(s)=-\frac{12}{s^{5}} \) 14. \( B(y)=c y^{-6} \) 15. \( g(t)=2 t^{-3 / 4} \) 16. \( h(t)=\sqrt[4]{t}-4 e^{t} \) 17. \( y=3 e^{x}+\frac{4}{\sqrt[3]{x}} \) 18. \( y=\sqrt{x}(x-1) \) 19. \( F(x)=2 answers -
1. \( \lim _{x \rightarrow-1} \frac{108\left(x^{2}+2 x\right)(x+1)^{3}}{\left(x^{3}+1\right)^{3}(x-1)} \)2 answers -
Solve \[ \begin{array}{l} y^{\prime \prime}+9 y^{\prime}+20 y=0, \quad y(0)=-3, \quad y^{\prime}(0)=10 \\ y(t)= \end{array} \]2 answers -
\( \begin{array}{l}x=5+t^{2}, \quad y=9+t^{3} \\ c(t)=\sqrt{\left.\frac{\left.\sqrt{\left(\frac{2 t \sqrt{4+9 t^{2}}-\frac{18 t^{3}}{\sqrt{4+9 t^{2}}}+2 t \sqrt{4+9 t^{2}}}{\left(t \sqrt{4+9 t^{2}}\ri2 answers -
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4. \( \left(3 x^{2} y+e^{y}\right) d x+\left[x^{3}+x e^{y}+\sin y\right] d y=0 \) 5. \( \left(2 x y+x^{3}+\left(y+x^{2}\right) \frac{d y}{d x}=0\right. \)2 answers -
12. Sketch the graph of the functions (a) \( f(x, y)=10-4 x-5 y \) (b) \( f(x, y)=\cos y \) (c) \( f(x, y)=2-x^{2}-y^{2} \) \( f(x, y)=\sqrt{4-4 x^{2}-y^{2}} \)2 answers -
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Given \( \quad y=\frac{(x+3)\left(x^{2}+2 x+5\right)}{\left(3 x^{2}+1\right)} \quad \) Calculate \( \mathbf{y}^{\prime} \mathbf{( 2 )} \)2 answers -
Differentiate the following function. \[ f(x)=2 x^{3}+6 x-\frac{1}{x}+3 e^{x}-\sin (x) \] A) \( f^{\prime}(x)=5 x^{2}+6+\frac{1}{x^{2}}+3 e^{x}+\cos (x) \) B) \( f^{\prime}(x)=6 x^{2}+6+\frac{1}{x^{2}2 answers -
Produce the equation of the line tangent of the given function at the specified point. \[ y=x^{2} e^{x} ; \quad P(1, e) \] A) \( y=(2 e) x-3 e \) B) \( y=(3 e) x-2 e \) C) \( y=(2 e) x-3 e^{2}+1 \) D)2 answers -
Complete the table. \begin{tabular}{l|l|l} \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{g}(\boldsymbol{x})) \) & \multicolumn{1}{|c|}{\( \boldsymbol{u}=\boldsymbol{g}(\boldsymbol{x}) \)} & \( \boldsym2 answers -
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Encuentre la forma parámetrica y la forma general del plano determinado por los siguientes puntos: 1. \( (4,-2,7) ;(2,6,9) \) y \( (3,1,-7) \) 2. \( (3,3,1) ;(4,6,2) \) y \( (-4,-3,-4) \)2 answers -
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Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ 6 x^{2}+7 y^{2}=10 \] (Express numbers in exact form. Use symbolic notatiol Assume that \( y \neq 0 \).) \[ y^{\prime}= \] \[ y^{\prime \prime}=-\4 answers -
Encuentre la forma parámetrica y la forma general del plano determinado por los siguientes puntos: 1. \( (4,-2,7) ;(2,6,9) \) y \( (3,1,-7) \) 2. \( (3,3,1) ;(4,6,2) \) y \( (-4,-3,-4) \)2 answers -
4. Sea \( \mathrm{F} \) un campo de fuerzas definido por \( F(x, y, z)=e^{3 x} \sin 2 y i+\frac{2}{3} e^{3 x} \cos 2 y j \). Calcule el trabajo hecho por \( \mathrm{F} \) sobre un objeto que se mueve0 answers -
6. Calcular la integral de superficie \( \iint_{S}\left(y^{2}+2 y z\right) d S \) donde \( \mathrm{S} \) es la porción del plano situado en el primer octante S: \( 2 x+y+2 z=8 \quad(10 \) pts.) Gráf2 answers -
7. Calcular el flujo de \( \mathrm{F} \) a través de la superficie cerrada. ( \( \mathrm{N} \) denota el vector unitario normal a la superficie dirigido hacia el exterior.) (15 pts.) Gráfica de la s2 answers -
Evaluate the integral. \[ \int \frac{\sqrt{y^{2}-9}}{y} d y, y>3 \] \[ \int \frac{\sqrt{y^{2}-9}}{y} d y= \]2 answers -
Differentiate using the Chain Rule. 1. \( y=\left(8 x^{2}-7\right)^{-40} \) 2. \( y=\sqrt[3]{7 x^{2}-x+2} \) 3. \( y=\frac{\left(2 x^{3}-x\right)^{3}}{(4 x+1)^{4}} \)2 answers