Calculus Archive: Questions from October 02, 2023
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Finding the derivative using the rules Differentiate the following functions. a. \( f(x)=\sin \left(e^{x^{2}}\right) \cdot \sin ^{-1} \sqrt{x} \) b. \( f(x)=\frac{\ln (2 x-1)}{\sec ^{4}(2 x-1)} \) c.1 answer -
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Finding the Domain and Range of a Function: \( f(x)=\frac{x-2}{x+4} \). Domain: all \( x \neq-4 \) Range: all \( y \neq 1 \) Domain: all \( x \neq 2 \) Range: all \( y \neq-1 \) Domain: all \( x \neq1 answer -
solve the given initial-value problem.
\( \begin{array}{l}\text { (30) } y^{\prime \prime}+4 y^{\prime}+4 y=(3+x) e^{-2 x} \\ y(0)=2 \quad y^{\prime}(0)=5 \\\end{array} \)1 answer -
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1. Let f(x, y) = ln(y² + x³). Compute D (2) ƒ(-2,-3). —3).
Let \( f(x, y)=\ln \left(y^{2}+x^{3}\right) \). Compute \( D_{\left\langle\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right\rangle} f(-2,-3) \).1 answer -
Calcule a integral de linha \( \int_{C} 2 x y^{2} d x+2 x^{2} y d y \), como caminho \( C \) dado por \( x=3 \cos t, y=5 \sin t, 0 \leq t \leq 2 \pi \).1 answer -
Find y' for y = x + 2x. e y"=0
Find \( y^{\prime \prime} \) for \( y=e^{x^{5}}+2 x \) \[ y^{\prime \prime}= \]1 answer -
Find y''. 1 y = tan (4x - 5) 16 y"=0
Find \( y^{\prime \prime} \). \[ y=\frac{1}{16} \tan (4 x-5) \] \[ y^{\prime \prime}= \]1 answer -
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d²y 2 dx 3x + 5y = 4 sin (y) Find d²y -0 2 dx
Find \( \frac{d^{2} y}{d x^{2}} \) \[ 3 x+5 y=4 \sin (y) \] \[ \frac{d^{2} y}{d x^{2}}= \]1 answer -
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\( \int_{r} 49 . \frac{d y}{d z}=\frac{(\sec (z) \csc (z)) \frac{d}{d z}[1]-(1) \frac{d}{2}[\sec (z) \csc (z)]}{(\sec (z) \csc (z))^{2}} \)1 answer -
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Solve the initial value problem
19. \( y^{\prime \prime}-y^{\prime}+4 y=0 ; y(-2)=1, y^{\prime}(-2)=3 \)1 answer -
(4) Given the function \( f(x, y)=4 x^{2} y^{2}-16 x^{2}+4 y \). Find the following: (a) \( f_{x}(x, y) \) (b) \( f_{x}(0, y) \) (c) \( f_{y}(x, y) \) (d) \( f_{y}(0, y) \)1 answer -
(5) Given the function \( f(x, y)=2 x e^{2 x^{2} y}-3 x^{5} y^{2} \). Find the following: (a) \( f_{x}(x, y) \) (b) \( f_{x}(0, y) \) (c) \( f_{y}(x, y) \) (d) \( f_{y}(0, y) \)1 answer -
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sania (0ar SOBO 27. If f(x) = (a) f(-3) (-12000.0) x2 4 3x - 2 if x < 0 ... if x = 0 find: if x > 0 (b) f(0) 00.0 (c) f(3)
7. If \( f(x)=\left\{\begin{array}{ll}-x^{2} & \text { if } x0\end{array}\right. \) (a) \( f(-3) \) (b) \( f(0) \) (c) \( f(3) \)1 answer -
2. Find all critical points of (a) \( f(x, y)=-x^{2}-y^{2}-4 x y \) (b) \( f(x, y)=3 x e^{y}-x^{3}-e^{3 y} \).1 answer -
please help
(4) Given the function \( f(x, y)=4 x^{2} y^{2}-16 x^{2}+4 y \). Find the following: (a) \( f_{x}(x, y) \) (b) \( f_{x}(0, y) \) (c) \( f_{3}(x, y) \) (d) \( f_{v}(0, y) \) (e) \( f_{n+}(x, y) \) (f)2 answers -
Let \( f(x, y, z)=\frac{x^{2}-5 y^{2}}{y^{2}+3 z^{2}} \). Then \[ f_{x}(x, y, z)= \] \[ f_{y}(x, y, z)= \] \[ f_{z}(x, y, z)= \]1 answer -
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A rock thrown from the top of a building is given an initial velocity of 20.0 m/s straight up. He The building is 50.0 m high and the rock barely clears the edge of the roof on its way down, as shown
A una roca que se lanza desde lo alto de un edificio se le da una velocidad inicial de \( 20.0 \mathrm{~m} / \mathrm{s} \) directo hacia arriba. El edificio tiene \( 50.0 \mathrm{~m} \) de alto y la r1 answer -
Aproximación polinomial de Lagrange Instrucciones: Aproximar la siguiente función dada de forma tabular por el método de Lagrange e interpolar el valor de la presión de vapor de agua a \( 30^{\cir1 answer -
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\( f(x)=\frac{4 x^{2} \tan x}{\sec x} \), find \[ f^{\prime}(x)=\frac{\left(8 x+\sec ^{2} x\right)-(\tan x)\left(4 x^{2} \tan x\right)}{(\sec x)^{2}} \]1 answer -
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translation: 1. Which of these integrals represent the area of the surface generated by rotating r=e^2θ, 0<= θ <= (π/2) around the line θ=π/2 2. Why aren't the others correct? !Resolve only
¿Cuál de estas integrales representa el área de la superficie generada al girar la curva \( r=e^{2 \theta}, \quad 0 \leq \theta \leq \frac{\pi}{2} \), alrededor de la línea \( \theta=\frac{\pi}{2}1 answer -
Find \( d y / d x \) by implicit differentiation. \[ \tan (x-y)=\frac{y}{7+x^{2}} \] \[ y^{\prime}= \]1 answer -
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3) Calculate the derivatives of the following functions y. (a) y = f(x)g(x) h(x) (b) y = (f(x) g(x))³ (c) y = (f(g(x)))³ (d) y = csc(f(2x) + g(h(x)))
3) Calculate the derivatives of the following functions \( y \). (a) \( y=\frac{f(x) g(x)}{h(x)} \) (b) \( y=(f(x) g(x))^{3} \) (c) \( y=(f(g(x)))^{3} \) (d) \( y=\csc (f(2 x)+g(h(x))) \)1 answer -
Calculate \( y^{\prime \prime} \) and \( y^{\prime \prime \prime} \). \[ y(x)=\frac{10 e^{x}}{x} \] \[ y^{\prime \prime}(x)=\mid \] \[ y^{\prime \prime \prime}(x)= \]1 answer -
Number 15 with detail
g. \( y=\frac{2}{3} x^{3 / 2}, \quad 0 \leqslant x \leqslant 2 \) 10. \( y=(x+4)^{3 / 2}, \quad 0 \leqslant x \leqslant 4 \) 11. \( y=\frac{2}{3}\left(1+x^{2}\right)^{3 / 2}, \quad 0 \leqslant x \leqs1 answer -
Please help. Thank you.
\( f(x, y)=2 x e^{y}-3 y e^{-x} \) \( { }_{x}(x, y) \) given \( f(x, y)=\frac{2 x}{x-3 y} \)1 answer -
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Given \( f(x, y)=-1 x^{5}+2 x^{2} y^{4}+1 y^{3} \) \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \]1 answer -
\( \begin{array}{l}\text { Given } f(x, y, z)=\sqrt{-6 x-4 y+2 z}, \\ f_{x}(x, y, z)=\mid \\ f_{y}(x, y, z)=\mid \\ f_{z}(x, y, z)=\mid\end{array} \)1 answer -
\( \begin{array}{l}\text { Given } f(x, y)=-x^{2}-5 x y^{3}+3 y^{4}, \mathrm{f} \\ f_{x}(x, y)= \\ f_{y}(x, y)=\end{array} \)1 answer -
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Given \( f(x, y)=3 x^{4}-3 x y^{5}-6 y^{3} \), find the following numerical values: \[ f_{x}(2,2)= \] \[ f_{y}(2,2)= \]1 answer -
In Problems \( 1-8 \), find \( d^{3} y / d x^{3} \). 1. \( y=x^{3}+3 x^{2}+6 x \) 2. \( y=x^{5}+x^{4} \) 3. \( y=(3 x+5)^{3} \) 4. \( y=(3-5 x)^{5} \) 5. \( y=\sin (7 x) \) 6. \( y=\sin \left(x^{3}\ri1 answer -
Zill, pág. 69 45. Cadena cayendo Una parte de una cadena de 8 pies de longitud está enrollada sin apretar alrededor de una clavija en el borde de una plataforma horizontal y la parte restante de la
Zill, pág. 69 45. Cadena cayendo Una parte de una cadena de 8 pies de longitud está enrollada sin apretar alrededor de una clavija en el borde de una plataforma horizontal y la parte restante de la1 answer -
Find the general solution for the differential equation. dy dx = y²e7x = A) y = C) y=- e7x 7 e7x 7 + C 1 +C B) y = D) y = 1 7e7x + C 1 e7x My + C
Find the general solution for the differential equation. A) \( y=-\frac{e^{7 x}}{7}+C \) B) \( y=\frac{1}{7 e^{7 x}+C} \) \( \frac{d y}{d x}=y^{2} e^{7 x} \) C) \( y=-\frac{1}{\frac{e^{7 e}}{7}+C} \)1 answer -
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Find \( y^{\prime} \) and \( y^{\prime \prime} \) \[ \begin{array}{l} y=(2+\sqrt{x})^{3} \\ y^{\prime}=\square \\ y^{\prime \prime}=\square \end{array} \] Find \( y^{\prime} \) and \( y^{\prime} \)1 answer -
Find the derivative of the function. \[ y=\sin (\theta+\tan (\theta+\cos (\theta))) \] \[ y^{\prime}= \]1 answer -
6. Find a function with the given gradient. (a) ▼ƒ(x, y, z) = i + 3ĵ + 5k . (b) Vg(x, y) = (y, r). (c) ▼h(x, y) = (2.ry, x² + 3y²) .
Find a function with the given gradient. (a) \( \nabla f(x, y, z)=\hat{i}+3 \hat{j}+5 \hat{k} \). (b) \( \nabla g(x, y)=(y, x) \). (c) \( \nabla h(x, y)=\left(2 x y, x^{2}+3 y^{2}\right) \).1 answer -
b) \( y=\tan \left(x^{2}-e\right) \tan ^{-1}\left(e^{\cos x}\right) \) [4 marks] c) \( y=\sin ^{5} \sqrt{\ln \left(x^{4}+1\right)} \) [4 marks] d) \( y=(x+1)^{x} \) [4 marks] a) \( y=\sqrt[3]{\sin \le0 answers -
c) \( y=\ln \left(e^{5 \cos x^{2}}\right) \sec ^{-1}\left(2^{x}\right) \) d) \( y=(x+1)^{\ln x} \) a) \( y=\tan (\ln x) \sqrt{x^{2}+\pi} \) b) \( y=\frac{\tan ^{-1}(x)}{1+x^{2}} \)0 answers