Calculus Archive: Questions from October 05, 2023
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calc 2
\( \begin{array}{l}\text { aluate } \int_{0}^{1} \frac{1}{16+(k x)^{2}} d x \\ \frac{1}{4 k} \tan ^{-1}\left(\frac{k}{4}\right) \\ 4 k \tan ^{-1}\left(\frac{k}{4}\right) \\ k \tan ^{-1}\left(\frac{k}{1 answer -
Solve both
Solve the DE \( y^{\prime \prime}-y^{\prime}-6 y=0 \) Solve the DE \( 4 y^{\prime \prime}+12 y^{\prime}+9 y=0 \)1 answer -
Solve Both
\( \begin{array}{l}y^{\prime \prime}-2 y^{\prime}+5 y=0 \\ y^{\prime \prime \prime}-3 y^{\prime \prime}+4 y^{\prime}-2 y=0\end{array} \)1 answer -
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number 16
\( y=f(u) \).] Then find the derivative \( d y / d x \). 1. \( y=\sqrt[3]{1+4 x} \) 2. \( y=\left(2 x^{3}+5\right)^{4} \) 3. \( y=\tan \pi x \) 4. \( y=\sin (\cot x) \) 5. \( y=e^{\sqrt{x}} \) 6. \( y1 answer -
find the derivative of the function number 40
32. \( F(t)=\frac{t^{2}}{\sqrt{t^{3}+1}} \) 33. \( G(x)=4^{c / x} \) 34. \( U(y)=\left(\frac{y^{4}+1}{y^{2}+1}\right)^{5} \) 35. \( y=\cos \left(\frac{1-e^{2 x}}{1+e^{2 x}}\right) \) 36. \( y=x^{2} e^1 answer -
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If y = (4x² + 2) (3 x ³ − 6 x), then dy dx = ?
\( y=\left(4 x^{2}+2\right)\left(3 x^{3}-6 x\right) \), then \( \frac{d y}{d x}=? \)1 answer -
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please calculate the derivatives of the following functions:
29. \( y=\sqrt{10 x+1} \) 31. \( y=5\left(7 x^{3}+1\right)^{-3} \) 33. \( y=\sec (3 x+1) \) 35. \( y=\tan e^{x} \) 37. \( y=\sin \left(4 x^{3}+3 x+1\right) \)1 answer -
differentation
\( \begin{array}{l}y=\left\{1+\left[1+(1+x)^{2}\right]^{3}\right\}^{4} \\ y=\left\{1+\left[1+(x+3)^{2}\right]^{3}\right\}^{4}\end{array} \)1 answer -
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Determina si la secuencia converge o diverge. Si converge, encuentre el límite. un norte = nsen(1/n)1 answer
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i just need number 10 quickly please.
Calculating First-Order Partial Derivatives In Exercises 1-22, find \( \partial f / \partial x \) and \( \partial f / \partial y \). 1. \( f(x, y)=2 x^{2}-3 y-4 \) 2. \( f(x, y)=x^{2}-x y+y^{2} \) 3.1 answer -
Find the limit, if it exists
\( \lim _{(x, y) \rightarrow(0,0)} \frac{x^{10}-y^{10}}{x^{5}+y^{5}} \)1 answer -
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Find \( \frac{\partial z}{\partial u} \) when \( u=-1, v=0 \), if \( z=\sin (x y)+x \sin (y), x=3 u^{2}+2 v^{2} \), and \( y=2 u v \). \[ \left.\frac{\partial z}{\partial u}\right|_{u=-1, v=0}= \] (Si1 answer -
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Instrucciones: Hallar la derivada de las siguientes funciones. Debe explicar y escribir claramente lo que realiza. (20 puntos) 1. \( f(x)=\frac{x}{\sqrt{7-3 x}} \) 2. \( y=\operatorname{sen} \sqrt{1+x1 answer -
131. Using a Function Consider the function f(x, y) = (x² + y²)2/3. Show that ƒ,(x, y) = { 3(x² + y²)¹/³' 0. (x, y) = (0,0) (x, y) = (0,0)*
131. Using a Function Consider the function \[ f(x, y)=\left(x^{2}+y^{2}\right)^{2 / 3} \text {. } \] Show that \[ f_{x}(x, y)=\left\{\begin{array}{ll} \frac{4 x}{3\left(x^{2}+y^{2}\right)^{1 / 3}} &1 answer -
(1 point) Solve the initial value problem. \( y^{\prime \prime}+11 y^{\prime}+30 y=0, \quad y(0)=1, y^{\prime}(0)=0 \). \( y(t)= \)1 answer -
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Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ \begin{array}{c} y=\sqrt{\sin (x)} \\ y^{\prime}=\frac{\csc (x)^{\left(\frac{1}{2}\right)} \cos (x)}{2} \times \\ y^{\prime \prime}=-\frac{\sin (x1 answer -
2] 3. Find and simplify an expression for \( d y / d x \). a) \( y=x^{-5} \ln (x) \) b) \( y=6^{\ln (x)}-2 \log _{4}\left(x^{3}\right) \) c) \( y=(2+\sin (x))^{x^{3}} \)1 answer -
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Graficar las siguientes funciones y hallar su respectiva serie de fourier.
\( f(x)=\left\{\begin{array}{rr}-x & -4 \leqq x \leqq 0 \\ x & 0 \leqq x \leqq 4\end{array}\right. \)1 answer -
Resuelve las siguientes ecuaciones diferenciales homogéneas, encuentra la solución general y la solución particular con las condiciones que se te presentan: 1. \( 4 y^{\prime \prime}+y^{\prime}=0 \1 answer -
Find y''. y = x(3x+4)5 y' =
Find \( y^{\prime \prime} \). \[ y=x(3 x+4)^{5} \] \[ y^{\prime \prime}= \]1 answer -
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Integrate the function. \[ \int \frac{y^{2}}{\left(49-y^{2}\right)^{3 / 2}} d y \] A. \( \frac{y}{\sqrt{49-y^{2}}}-\sin ^{-1}\left(\frac{y}{7}\right)+C \) B. \( \sqrt{49-y^{2}}-\sin ^{-1}\left(\frac{y1 answer -
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\[ f(x)=\frac{\tan x-4}{\sec x} \] find \( f^{\prime}(x) \). \[ \frac{\sec ^{3} x-(\tan x-4)(\sec x \tan x)}{(\sec x)^{2}} \] Find \( f^{\prime}\left(\frac{\pi}{2}\right) \).1 answer -
3. (8 points) For \( f(x, y)=x^{3} y^{2}+\frac{y}{y-x} \), find \( f_{y y}(x, y) \) and \( f_{x y}(x, y) \).1 answer -
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Determine el momento en \( \mathrm{A} \) \[ \begin{array}{c} \mathrm{F}_{1}=10 \mathrm{kN} \\ \mathrm{F}_{2}=4 \mathrm{kN} \\ \mathrm{d}=2.8 \mathrm{~m} \\ \theta=44^{\circ} \end{array} \]1 answer -
82. Let \( f(x, y)=\left\{\begin{array}{ll}x y \frac{x^{2}-y^{2}}{x^{2}+y^{2}}, & \text { if }(x, y) \neq 0, \\ 0, & \text { if }(x, y)=0 .\end{array}\right. \) The graph of \( f \) is shown on page 71 answer -
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d dx (3x tan (x²)) » x=1
\( \left[\frac{d}{d x}\left(3 x-\tan ^{-1}\left(x^{2}\right)\right)\right]_{x=1} \)1 answer -
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Find the solution y(t) of the initial value problem y" - 8 y' + 16 y = 8e²t, y(0) y(0) = 3, y' (0) = 2.
Find the solution \( y(t) \) of the initial value problem \[ y^{\prime \prime}-8 y^{\prime}+16 y=8 e^{2 t}, \quad y(0)=3, \quad y^{\prime}(0)=2 \]1 answer -
\[ \int_{0}^{3} \int_{-3}^{3} \int_{-\sqrt{9-x^{2}}}^{\sqrt{9-x^{2}}} \frac{1}{\left(x^{2}+y^{2}\right)^{1 / 2}} d y d x d z \] Evaluate the intergal1 answer -
Find \( y^{\prime \prime} \) by implicit differentiation. \[ \begin{array}{l} \quad 7 x^{2}+y^{2}=8 \\ y^{\prime \prime}=-\frac{7}{y} \end{array} \]1 answer -
CO 6 Solve the linear differential equation (0.5 Points) dy dx 2y cot 2x = 1 - 2x cot 2x − 2 csc 2x - O y = x + cos2x + c sin 2x Oy y = x - cos 2x + c sin 2x O y = x + y cos 2x + c sin 2x O y = x -
Solve the linear differential equation (0.5 Points) \[ \frac{d y}{d x}-2 y \cot 2 x=1-2 x \cot 2 x-2 \csc 2 x \] \[ y=x+\cos 2 x+c \sin 2 x \] \[ y=x-\cos 2 x+c \sin 2 x \] \[ y=x+y \cos 2 x+c \sin 21 answer -
Solve the exact \( \mathrm{DE} \). (0.5 Points) \[ \left(y^{2}-2 x\right) d x+(2 x y+1) d y=0 \] \[ x y^{2}+x^{2}-2 y=C \] \[ x y^{2}-x^{2}+2 y=C \] \[ x y^{2}+x^{2}-y=C \] \[ x y^{2}-x^{2}+y=C \]1 answer -
3. (8 points) For \( f(x, y)=x^{3} y^{2}+\frac{y}{y-x} \), find \( f_{y y}(x, y) \) and \( f_{x y}(x, y) \).1 answer -
Find \( \left.\frac{d y}{d x}\right|_{(0,-2)} \) if \( x^{2} y=(y+2)+x y \sin x \). 0 \( -\frac{1}{2} \) \( -1 \) 11 answer -
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Help.me find the domain, range, and graph for 15,18,31
15. \( f(x, y)=y^{2}+1 \) 16. \( f(x, y)=e^{-y} \) 17. \( f(x, y)=9-x^{2}-9 y^{2} \) 18. \( f(x, y)=1+2 x^{2}+2 y^{2} \) \( f(x, y)=\sqrt{y^{2}-x^{2}} \)1 answer -
(1 point) Let \( f(x, y, z)=\frac{x^{2}-3 y^{2}}{y^{2}+2 z^{2}} \). Then \[ \begin{array}{l} f_{x}(x, y, z)= \\ f_{y}(x, y, z)= \\ f_{z}(x, y, z)= \end{array} \]1 answer -
Find y' for the following function. y = 2 csc x sec x
Find \( y^{\prime \prime} \) for the following function. \[ y=2 \csc x \sec x \]1 answer -
[12] 3. Find and simplify an expression for \( d y / d x \). a) \( y=x^{-5} \ln (x) \) b) \( y=6^{\ln (x)}-2 \log _{4}\left(x^{3}\right) \) c) \( y=(2+\sin (x))^{x^{3}} \)1 answer -
Find \( \frac{d^{2} y}{d x^{2}} \) if \( y=7 \sin x \cos x \) \[ \frac{d^{2} y}{d x^{2}}= \] Find \( \frac{d^{2} y}{d x^{2}} \) if \( y=4 x \cos x \) \[ \frac{d^{2} y}{d x^{2}}= \]1 answer -
#109 #113 #115
For the following exercises, find the critical points in the domains of the following functions. 108. \( y=4 x^{3}-3 x \) 109. \( y=4 \sqrt{x}-x^{2} \) 110. \( y=\frac{1}{x-1} \) 111. \( y=\ln (x-2) \1 answer -
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Find y for the following function. y = 4 cos x sin x
Find \( y^{\prime \prime} \) for the following function \[ y=4 \cos x \sin x \]1 answer -
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Integrar con método de sustitución
\( \int \operatorname{sen}^{5} \frac{x}{3} \cos \frac{x}{3} d x \)1 answer -
#28
In Problems \( 65-72 \) solve the given initial-value problem. 65. \( y^{\prime \prime}-64 y=16, \quad y(0)=1, y^{\prime}(0)=0 \) 66. \( y^{\prime \prime}+y^{\prime}=x, \quad y(0)=1, y^{\prime}(0)=0 \1 answer -
Solve the separable initial value problem. 1. \( y^{\prime}=2 x \cos \left(x^{2}\right)\left(1+y^{2}\right), y(0)=2 \Rightarrow y \) 2. \( \quad y^{\prime}=4 e^{2 x}\left(1+y^{2}\right), y(0)=-2 \Righ1 answer -
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