Calculus Archive: Questions from October 30, 2023
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if xy^2 + e^y = xy, compute y'
If \( x y^{2}+e^{y}=x y \), compute \( y^{\prime} \) None of the other choices (B) \( y^{\prime}=\frac{y^{2}-2 y}{2 x+2 x y-e^{y}} \) (C) \( y^{\prime}=\frac{y^{2}-y}{x+2 x y+e^{y}} \) (D) \( y^{\prim1 answer -
63-78 Find the derivative of the function. Simplify where possible. 63. f(x) = sin(5x) 65. y = tan ¹√√x-1 67. y = (tan ¹x)² 69. h(x) = (arcsin x) In x 71, f(2)=sin(22) 64. g(x) = sec ¹(e¹) 66
63-78 Find the derivative of the function. Simplify where possible. 63. \( f(x)=\sin ^{-1}(5 x) \) 64. \( g(x)=\sec ^{-1}\left(e^{x}\right) \) 65. \( y=\tan ^{-1} \sqrt{x-1} \) 66. \( y=\tan ^{-1}\lef1 answer -
Find \( y^{\prime} \) where \( y=\sin \left(x e^{11 x}\right)-14^{\csc x} \) Answer: \[ \begin{array}{l} y^{\prime}=\cos \left(x e^{11 x}\right)\left(e^{11 x}+11 x e^{11 x}\right)+14^{\csc x} \ln (14)1 answer -
Rewrite the following iterated integral using five different orders of integration. \[ \int_{-4}^{4} \int_{-\sqrt{16-x^{2}}}^{\sqrt{16-x^{2}}} \int_{x^{2}+y^{2}}^{16} g(x, y, z) d z d y d x \] \[ \beg1 answer -
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Una masa de aire frío se aproxima a un campus universitario de modo que si la temperatura es \( \mathrm{T}(\mathrm{t}) \) grados Fahrenheit \( t \) horas después de la media noche, entonces: \[ T(t)1 answer -
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Si \( f \) y \( g \) son derivables, entonces \[ \frac{d}{d x}[f(x) g(x)]=f^{\prime}(x) g^{\prime}(x) \] Verdadero Falso1 answer -
Si \( f \) tiene un valor mínimo absoluto en \( c \), entonces \( f^{\prime}(c)=0 \). Verdadero Falso1 answer -
45-60 Find the limit. 45. \( \lim _{x \rightarrow 0} \frac{\sin 5 x}{3 x} \) 47. \( \lim _{t \rightarrow 0} \frac{\sin 3 t}{\sin t} \)1 answer -
49-50 Suponga que todas las funciones dadas son derivables. 49. Si \( z=f(x, y) \), donde \( x=r \cos \theta \) y \( y=r \operatorname{sen} \theta \), (a) encuentre \( \partial z / \partial r \) y \(1 answer -
find the following partial derivative
(c) \( f_{x}(x, y) \) and \( f_{y}(x, y) \), where \( f(x, y)=e^{x y} \cdot \ln (y) \) \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \]1 answer -
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\( \iint_{R} 2 x-y d A ; \quad R=\left\{(x, y) \mid x^{2}+y^{2} \leq 4, x \geq 0, y \geq 0\right\} \)1 answer -
find the derivative
\( \begin{array}{l}y=\sqrt{\frac{x}{x+1}} \\ y=e^{\tan \theta} \\ g(u)=\left(\frac{u^{3}-1}{u^{3}+1}\right)^{8}\end{array} \) \( \begin{array}{l}y=e^{\tan \theta} \\ g(u)=\left(\frac{u^{3}-1}{u^{3}1 answer -
Using the following properties of a twice-differentiable function \( y=f(x) \), select a possblo praph of 11 answer -
find y by implicit diffrentiation
\( y=\sqrt{\frac{x}{x+1}} \) 39. \( x^{2}+4 y^{2}=4 \) 41. \( \sin y+\cos x=1 \)1 answer -
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22. lim (x₁y)→(1,0) y ln y x Ix. vl
22. \( \lim _{\left(x_{1} y\right) \rightarrow(1,0)} \frac{y \ln y}{x} \)1 answer -
Find the values of the function. \[ g(x, y)=x^{2} e^{4 y} \] (a) \( g(-4,0) \) (b) \( g\left(4, \frac{1}{4}\right) \)1 answer -
blems B 4 5 6 7 18 9 10 (1 point) Find y by implicit differentiation. Match the equations defining y implicitly with the letters labeling the expressions for y. 1. 3x sin y + 2 cos 2y = 6 cos y 2. 3x
(1 point) Find \( y^{\prime} \) by implicit differontiation. Match the equations defining \( y \) implicity with the letters labeling the expressions for \( y \). 1. \( 3 x \sin y+2 \cos 2 y=6 \cos y1 answer -
\( f(x, y)=\sqrt{4 x^{2}+2 y^{2}} \) \( f_{x}(-1,1)= \) Given \( f(x, y)=x^{3}+5 x y^{6}+3 y^{2} \) \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \]1 answer -
Given \( f(x, y)=-6 x^{6}+3 x^{2} y^{5}+4 y^{4} \) \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] Given \( f(x, y)=7 x^{2} \ln \left(y^{5}\right) \) \[ \begin{array1 answer -
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For f(x, y), find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously. f(x, y) = x² - xy + y² - 5x + y (x, y) =
For \( f(x, y) \), 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}-x y+y^{2}-5 x+y \\ (x, y)=() \end{arra1 answer -
\( \begin{array}{l}\text { Integrate } \iint_{R} x \sec ^{2} y d A \text { where } R=\left\{(x, y) \mid 0 \leq x \leq 3,0 \leq y \leq \frac{\pi}{6}\right\} \\ \iint_{R} x \sec ^{2} y d A=\end{array} \1 answer -
(1 point) Find \( y^{\prime} \) by implicit differentiation. Match the equations defining \( y \) implicitly with the letters labeling the expressions for \( y^{\prime} \). 1. \( 4 x \cos y+5 \cos 2 y1 answer -
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luate the integral \( \int \cos ^{3}(3 x) \sin ^{3}(3 x) d x \) \[ \begin{array}{l} \frac{1}{3}\left(\frac{\sin ^{4}(3 x)}{4}+\frac{\sin ^{6}(3 x)}{6}\right)+c . \\ \frac{1}{3}\left(\frac{\sin ^{4}(31 answer -
Find the General Solution of:
\( y^{\prime \prime \prime}+y^{\prime \prime}+y^{\prime}+y=1+e^{x}+e^{-x}+e^{2 x}+e^{-2 x} \)1 answer -
Express the integral ∭Ef(x,y,z)dV∭ as an iterated integral in six different ways, where E is the solid bounded by z=0, x=0, z=y−6x, and y=18.
\( \begin{array}{l}\text { 1. } \int_{a}^{b} \int_{g_{1}(x)}^{g_{2}(x)} \int_{h_{1}(x, y)}^{h_{2}(x, y)} f(x, y, z) d z d y d x \\ a=0 b=\frac{(y-z)}{6} \\ g_{1}(x)=\quad g_{2}(x)= \\ h_{1}(x, y)=0 h_1 answer -
\( \begin{array}{c}\int_{0}^{2} f(x, y) d x \text { and } \int_{0}^{3} f(x, y) d y . \\ f(x, y)=11 y \sqrt{x+2}\end{array} \)1 answer -
Exprese A en forma implícita como una función de a, b y c, luego calcule \( \partial \mathrm{A} / \partial \mathrm{a} \mathrm{y} \) \( \partial \mathrm{A} / \partial \mathrm{b} \).1 answer -
point) Find y' by implicit differentiation. Match the equations defining y implicitly with he letters labeling the expressions for y'. A. y' = B. y' c. y' = D. y' S = 1. 5x sin y + 6 sin 2y = 6 cos y
point) Find \( y^{\prime} \) by implicit differentiation. Match the equations defining \( y \) implicitly with e letters labeling the expressions for \( y^{\prime} \). 1. \( 5 x \sin y+6 \sin 2 y=6 \c1 answer -
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11. (10 points) Dibuje la curva \( r=3-4 \cos (\theta) \). Bono: (10 Puntos): Halle el área de la región dentro de \( r=3 \cos (\theta) \) y fuera de \( r=2-\cos (\theta) \).1 answer -
9. “Halle ecuacion de la recta tangente a: x=t^3, y=t^2; en el punto (1,1)”
9. (10 points) Halle ecuación de la recta tangente as \( x=t^{3}, y=\theta_{\text {; }} \) en al punto \( (0,1) \), 10. (10 points) Halle la región en el plano que consiste de los puntos cuyas coord1 answer -
(10 points) Halle el largo del arco \( \ln \left(1-x^{2}\right), 0 \leq x \leq \frac{1}{2} \). (10 points) Elimine el parámetro para hallar la ecuación cartesiana de la curva y dibuje: \[ x(t)=\cos1 answer -
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5. (10 points) Usando el criterio de series divergentes, determine si converge o no. \[ \sum_{n=0}^{\infty}(-1)^{n} \frac{1+4^{n}}{5^{n}} \] 6. (10 points) Halle el área de la superficie que se obtie1 answer -
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SCALCET9 14.XP.3.017. Find the first partial derivatives of the function. \[ f(x, y, z)=x z-7 x^{3} y^{7} z^{4} \] \[ f_{x}(x, y, z)= \] \[ f_{y}(x, y, z)= \] \[ f_{z}(x, y, z)= \]1 answer -
2. Given that y depends on x, find y' of 3x² + 6xy = 2y² + 2
2. Given that \( y \) depends on \( x \), find \( y^{\prime} \) of \( 3 x^{2}+6 x y=2 y^{2}+2 \) (A) \( y^{\prime}=\frac{6(x+y)}{4 y-6 x} \) (B) \( y=\frac{6(x+y)-2}{4 y-6 x} \) (C) \( y=\frac{6(x+y)}1 answer -
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( 1 point) Find \( y^{\prime} \) by implicit differentiation. Match the equations defining \( y \) implicitly with the letters labeling the expressions for \( y^{\prime} \). 1. \( 5 x \cos y+6 \cos 21 answer -
PLEASE HELP!! Compute y' (2) when y = xg(x) x² + f(x), and (2) = -1, f'(2) = 1; g(2) = 2, g'(2) = 1.
Problem 24 (Data analysis) Compute \( y^{\prime}(2) \) when \( y=\frac{x g(x)}{x^{2}+f(x)} \), and \[ f(2)=-1, \quad f^{\prime}(2)=1 ; \quad g(2)=2, \quad g^{\prime}(2)=1 . \]1 answer -
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thank you
( 1 point) Find \( y^{\prime} \) by implicit differentiation: Match the equations defining \( y \) implicitly with the letters labeling 1. \( 5 x \sin y+7 \sin 2 y=6 \cos y \) 2. \( 5 x \cos y+7 \cos1 answer -
(1 point) Find \( y^{\prime} \) by implicit differentiation. Match the equations defining \( y \) implicitly with the letters labeling the expressions for \( y^{\prime} \). 1. \( 7 x \cos y+7 \cos 2 y1 answer -
Find \( y^{\prime}, y^{\prime \prime} \) and \( y^{\prime \prime \prime} \) if \( y=x^{3}-6 x^{2}-5 x+3 \)1 answer -
find the derivative of y
\( \begin{array}{l}\text { c. } y=x e^{7 x} \quad(P-r u l e) \quad U=7 x \\ \text { first: } x \quad \text { second: } e^{7 x} \quad u^{\prime}=7 \\ \left(e^{1 x}\right)(1)^{1}+(x)( \\\end{array} \)1 answer -
Ejercicio 4. El precio del petróleo crudo durante el periodo \( 2000-2010 \) puede aproximarse por medio de la función: \[ P(t)=6 t+18 \text {, dólares por barril, } \quad(0 \leq t \leq 10) \] dond1 answer -
Ejercicio 5. Parumount Electronics tiene un ingreso anual dado por: \[ P=-100000+5000 q-0.25 q^{2}, \] dólares donde \( q \) es el número de laptops vendidas al año. El número de laptops que puede1 answer -
1.5. Derivadas de logaritmos y exponenciales Ejercicio 6. El gasto total en investigación y desarrollo por la industria en Estados Unidos durante el periodo 2002 - 2012 puede aproximarse mediante la1 answer -
La sustitución \( u=x^{2}, x=\sqrt{u}, d x=\frac{d u}{2 \sqrt{u}} \), parece conducir al resultado \[ \int_{-1}^{1} x^{2} d x=\frac{1}{2} \int_{1}^{1} \sqrt{u} d u=0 . \] ¿Cree usted que éste sea e1 answer -
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\[ \int_{1}^{4} \int_{0}^{6} \frac{\sqrt{y}}{x^{2}} d y d x \] Provide an exact answer: of \( \left(1-\frac{1}{4}\right) \cdot \frac{2}{3} \cdot 6^{\frac{3}{2}} \) Now numerical calculation to 4 decim1 answer -
14. Find \( y^{\prime} \) if \( y=2 x+\sqrt{x^{4}-7 x+2} \). 15. If \( g(x)=x \sqrt{x^{2}+5} \), find \( g^{\prime}(x) \) and \( g^{\prime}(2) \).1 answer -
calculus help
Find the domain of the function. \[ f(x, y, z)=\frac{x y z}{\sqrt{2 x^{2}+5 y^{2}+9 z^{2}}} \] The domain is \[ \begin{array}{l} \{(x, y, z) \mid x \neq 0, y \neq 0, z \neq 0\} \\ \{(x, y, z) \mid(x,1 answer -
Take each derivative a. \( y=3 x^{5}-7 x \) b. \( y=\sqrt{x^{3}}-\frac{1}{x} \) c. \( y=\tan (2 x) \) d. \( y=\sin (x) \cos (x) \) e \( y=\frac{1-x^{2}}{x^{2}-1} \) f. \( y=\frac{1-x^{2}}{x^{2}-1.1} \1 answer -
Find y' and y" by implicit differentiation. 4x³ - 5y³ = 7 y' y" = = 4x2 51² 2 L X
Find \( y^{\prime} \) and \( y^{\prime \prime} \) by implicit differentiation. \[ \begin{array}{l} 4 x^{3}-5 y^{3}=7 \\ \frac{4 x^{2}}{5 y^{2}} \end{array} \]1 answer