Calculus Archive: Questions from November 03, 2023
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\( x=10 u+4 v+8 w, y=10 u+9 v-4 w \), and \( z=8 u-10 v-8 w \) implies \( \frac{\partial(x, y, z)}{\partial(u, v, w)}= \)1 answer -
\( x=u v-7 u, y=7 u v-3 u v w \), and \( z=-2 u v w \) implies \( \frac{\partial(x, y, z)}{\partial(u, v, w)}= \)1 answer -
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Find \( \frac{d y}{d x} \) for \( y=8 \sec x \tan x \) \[ \frac{d}{d x}(8 \sec x \tan x)= \] Find \( \frac{d y}{d x} \) for \( y=x^{7} \sin x \)1 answer -
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finding the derivative
\( \begin{array}{ll}y=\ln (1 / x) & \text { 18. } y=\ln (10 / x) \\ y=\ln (\ln x) & \text { 20. } y=x \ln x-x \\ y=\log _{4}\left(x^{2}\right) & \text { 22. } y=\log _{5} \sqrt{x} \\ y=\log _{2}(1 / x1 answer -
Find y' given x^2 times y^4 plus y = 8
Find \( y^{\prime} \) given \( x^{\wedge} 2 \) times \( y^{\wedge} 4 \) plus \( y=8 \)1 answer -
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Find the derivative of \( y=\ln \left(\frac{\sqrt{7+13 x^{2}}}{x^{7}}\right) \). Answer: \( y^{\prime}= \)1 answer -
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Select the domain of the given function. \[ \begin{array}{r} f(x, y, z)=\frac{4 z x}{\sqrt{13-x^{2}-y^{2}-z^{2}}} \\ \text { Domain }=\left\{(x, y, z) \mid x^{2}+y^{2}+z^{2}>13\right\} \\ \text { Doma1 answer -
Find \( y^{\prime} \) where \( y=\cos ^{9} x+e^{\sin (6 x+14)} \) Answer: \[ \begin{array}{l} y^{\prime}=9 \cos ^{8} x-e^{\cos (6 x+14)} \\ y^{\prime}=9 \sin ^{8} x \cos x-6 e^{\cos (6 x+14)} \\ y^{\p1 answer -
Find \( y^{\prime} \) where \( y=6 \cos ^{-1}(\sin (13 x))-\cot ^{-1}(15 x) \) Answer: \[ \begin{aligned} y^{\prime} & =-78-\frac{1}{1+225 x^{2}} \\ y^{\prime} & =\frac{-78 \cos (13 x)}{\sqrt{1-\sin ^1 answer -
( 1 point) Find \( y \) as a function of \( t \) if \[ 36 y^{\prime \prime}+12 y^{\prime}+y=0 \] \[ \begin{array}{l} y(\Pi)=8 \quad v^{\prime}(\Pi)=5 . \\ y \end{array} \]1 answer -
(1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}+9 y^{\prime}=0 \text {, } \] \[ \begin{array}{l} y(0)=-7, \quad y^{\prime}(0)=-3, \quad y^{\prime \prime}(0)=-36 . \\ v(x1 answer -
( 1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-9 y^{\prime \prime}-y^{\prime}+9 y=0 \] \[ y(0)=-1, \quad y^{\prime}(0)=4, \quad y^{\prime \prime}(0)=239 . \]1 answer -
f(x,y)=4x³y²– 2xycos(x² + 5y) find fx
\[ f(x, y)=4 x^{3} y^{2}-2 x y \cos \left(x^{2}+5 y\right) \] find \( f_{x} \)1 answer -
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Express the integral \( \iiint_{E} f(x, y, z) d V \) as an iterated integral in six different ways, where \( \mathrm{E} \) is the solid bounded by \( z=0, x=0, z=y-4 x \) and \( y=12 \). 1. \( \int_{a1 answer -
Express the integral \( \iiint_{E} f(x, y, z) d V \) as an iterated integral in six different ways, where \( \mathrm{E} \) is the solid bounded by \( z=0, z=6 y \) and \( x^{2}=36-y \). 1. \( \int_{a}1 answer -
3. Sea \( f(x, y, z)=e^{\sqrt{m^{2}+n^{2}} x} \cos (m y) \operatorname{sen}(n z) \). Calcular las siguientes derivadas: a) \( \frac{\partial^{2} f}{\partial x^{2}} \) b) \( \frac{\partial^{2} f}{\part1 answer -
1. Dada la curva \( \vec{r}(t)=t^{2} \vec{i}+\frac{2}{3}(2 t+1)^{\frac{3}{2}} \vec{j} \). Calcular el valor de la siguiente integral. \[ L=\int_{a}^{b}\left\|r^{\prime}(t)\right\| d t \] Donde \( L \)1 answer -
Find \( y^{\prime} \) where \( y=7 \cos ^{-1}(\sin (7 x))-\cot ^{-1}(5 x) \) Answer: \[ \begin{aligned} y^{\prime} & =-49-\frac{5}{1+25 x^{2}} \\ y^{\prime} & =\frac{49}{\sqrt{1-\sin ^{2}(7 x)}}-\frac1 answer -
Find \( y^{\prime} \) where \( y=\left(\tan \left(25 x^{2}+23\right)\right) \sqrt{15 x^{3}+11} \) Answer. \[ \begin{array}{l} y^{\prime}=50 x \sec ^{2}\left(25 x^{2}+23\right) \frac{45 x^{2}}{2 \sqrt{1 answer -
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Find the derivative of the function. (√sin(tan(3x)) y' = y = = COS
Find the derivative of the function. \[ y=\cos (\sqrt{\sin (\tan (3 x))}) \]1 answer -
(1 point) Find \( y \) as a function of \( x \) if \[ \begin{array}{l} y^{\prime \prime \prime}+36 y^{\prime}=0, \\ y(0)=-8, y^{\prime}(0)=-12, y^{\prime \prime}(0)=36 . \\ y(x)= \end{array} \]1 answer -
Los pasos a seguir son los siguientes: 1.- Usa los datos de la tabla anterior para obtener la razón de cambio de las poblaciones de cada una de las especies respecto al tiempo. ¿Cómo lo harÃas? ¿1 answer -
1) Considera la función \( f(x)=\frac{2 x^{2}-1}{x-1} \) 2) Encuentre el lÃmite de \( f(x) \) cuando \( x \) se acerca a 1 . (1 punto) Es decir calcula \( \lim _{x \rightarrow 1} \frac{2 x^{2}-1}{x-1 answer -
Find the derivative of each function. (a) \( y=10 e^{x} \) (b) \( y=e^{x^{2}-3 x+7} \) (c) \( y=(x+2)^{3} e^{-5 x} \) (d) \( y=\frac{x^{2} e^{2 x}}{x+e^{3 x}} \) (e) \( y=3 \cdot 7^{\sqrt{x}} \)1 answer -
find the derivative of the functions
(a) \( y=15 \ln x \) (b) \( y=x^{4} \ln \left(x^{3}+e^{-x}\right) \) (c) \( y=\frac{e^{5 x}}{\ln (3 x)} \) (d) \( y=\log _{7} \sqrt{4 x-3} \) (e) \( y=(1+\ln |2 x-1|)^{5} \) (f) \( y=\log _{3}\left|x+1 answer -
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1. Differentiate. (a) \( g(\theta)=e^{\theta}(\tan \theta-\theta) \) (b) \( y=\frac{\cos x}{1-\sin x} \) (c) \( y=\frac{\sin t}{1+\tan t} \)1 answer -
2. Find the limit. (a) \( \lim _{t \rightarrow 0} \frac{\tan 6 t}{\sin 2 t} \) (b) \( \lim _{x \rightarrow 0} \frac{\sin 3 x \sin 5 x}{x^{2}} \)1 answer -
2. Halle los valores exactbs de \( \operatorname{sen}\left(\frac{\alpha}{2}\right), \cos \left(\frac{\alpha}{2}\right) \) y \( \tan \left(\frac{\alpha}{2}\right), \bullet \) si \( \pi1 answer -
Find \( d y / d x \) by implicit differentiation. (a) \( 2 x^{2}+x y-y^{2}=2 \) (b) \( \cos (x y)=1+\sin y \) (c) \( x \sin y+y \sin x=1 \)1 answer -
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Find the Jacobian of the transformation. \[ x=7 v+7 w^{2}, \quad y=8 w+8 u^{2}, \quad z=9 u+9 v^{2} \] \[ \frac{\partial(x, y, z)}{\partial(u, v, w)}= \]1 answer -
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Plantea el modelo que representa a la población \( P \) en función del tiempo \( t \). La tabla siguiente muestra la población (en millones de personas) de una ciudad para diferentes años. Respond1 answer -
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(1 point) Let \( f(x, y, z)=\frac{x^{2}-3 y^{2}}{y^{2}+4 z^{2}} \). Then \[ \begin{array}{l} f_{x}(x, y, z)= \\ f_{y}(x, y, z)= \\ f_{z}(x, y, z)= \end{array} \]1 answer -
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Show work please
For the following, determine \( \mathrm{dy} / \mathrm{dx} \). \[ y=\frac{1+\ln y}{1-\ln x} \]1 answer -
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