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Calculus Archive: Questions from September 28, 2022

• Differential equation
  \( \longrightarrow \) power 2 (4 points) Solve: \( y^{\prime}=2 x y /\left(y^{2}-x^{2}\right) \) ppower 2 Pet \( u=y \quad: y=u x, y^{\prime}=u^{\prime} x+u \)
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• find y'
  1-54 Calculate \( y^{\prime} \) (1.) \( y=\left(x^{2}+x^{2} y^{4}\right. \) (2.) \( =\frac{1}{\sqrt{t}} \quad \frac{1}{\sqrt{x}} \) (3.) \( y=\frac{x^{2}-x+2}{\sqrt{x}} \) (4.) \( v=\frac{\tan \pi}{1=
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• graph and show steps
  Trace la gráfica de: \[ 3 x-5 y=15 \]
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  \( y=\frac{3 \sqrt{x+1}-\cos (2 x)}{4+\cot (x)} \)
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• asap
  1. (12) Find the length of the curve \( y=\frac{1}{3}\left(2+x^{2}\right)^{3 / 2} \) over \( 0 \leq x \leq 3 \) \( y=\frac{1}{3}\left(2+x^{2}\right)^{3 / 2} \) over \( 0 \leqslant x \leqslant 3 \quad
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  8. Maximize \[ p=x+2 y \] subject to \[ \begin{aligned} 30 x+20 y & \leq 600 \\ 0.1 x+0.4 y & \leq 4 \\ 0.2 x+0.3 y & \leq 4.5 \\ x \geq 0, y \geq 0 \end{aligned} \]
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  10. Minimize \[ c=0.4 x+0.1 y \] subject to \[ \begin{array}{l} 30 x+20 y \geq 600 \\ 0.1 x+0.4 y \geq 4 \\ 0.2 x+0.3 y \geq 4.5 \\ x \geq 0, y \geq 0 \end{array} \]
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  Escriba la función compuesta en la forma \( f(g(x)) \). [Identifique la función interior \( u=g(x) \) y la exterior \( y=f(u) \).] \[ y=\left(1-x^{2}\right)^{3} \] \[ (g(x), f(u))=( \]
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• 4. If f (x, y) = x3 −12x + y2 −10y find all points where ||∇f|| = 0 .
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  1. Let \( f(x, y)=\ln \left(y^{2}+x^{3}\right) \). Compute \( D\left\langle\frac{1}{\left.\sqrt{2}, \frac{1}{\sqrt{2}}\right\rangle} f(-2,-3)\right. \).
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• The exact length of the curve
  \( x=\frac{1}{3} \sqrt{y}(y-3), \quad 1 \leqslant y \leqslant 9 \)
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• HELP PLEASE
  Differentiate. \[ \begin{array}{c} y=x^{4}+\cot (x) \\ y^{\prime}=4 x^{3}-\cos \times \end{array} \]
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• The momentum in a particle is given by ........, where ^p is in kg*m/s and t is in seconds. Find the magnitude of the force at t=2.0s.
  La cantidad de movimiento en una particula está dada por \( \Delta p=3 t^{2} i-2 t^{3} j \), donde \( \Delta p \) está en \( \mathrm{kg}^{*} \mathrm{~m} / \mathrm{s} \) y \( t \) en segundos. Halle
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• find y'
  48. \( y=\frac{\sin m x}{x} \) 49. \( y=\ln (\cosh 3 x) \) 50. \( y=\ln \left|\frac{x^{2}-4}{2 x+5}\right| \) 51. \( y=\cosh ^{-1}(\sinh \) 52. \( y=x \tanh ^{-1} \sqrt{x} \) 53. \( y=\cos \left(e^{\s
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  If \( \ln (\sec \theta)=\frac{1}{2} \ln (10) \)
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• please do 21&23
  21. \( x=\frac{1}{\sqrt{1+y^{2}}}, x=0, y=-1 \), and \( y=1 \); about the \( y \)-axis 23. \( y=x \) and \( y=2 \sqrt{x} \); about the \( x \)-axis
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  First order linear system: (a) \( y^{\prime}-2 \cdot y=e^{2 x}, y(0)=2 \), (b) \( y^{\prime}-2 \cdot y=x, y(0)=2 \), (c) \( \frac{1}{x} \cdot y^{\prime}-\frac{2 \cdot y}{x^{2}}=x \cdot \cos (x), y(\pi
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  \( y=\tan \left(\cos \left(\sqrt{3^{x}+x^{2}}\right)\right) \). Find \( \frac{d y}{d x} \)
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  If \( \frac{d y}{d x}=\frac{x}{\sqrt{9+x^{2}}} \) and \( y(4)=5 \), which equation defines \( y \) ? A. \( y=\frac{1}{\sqrt{9+x^{2}}} \) B. \( y=\sqrt{9+x^{2}} \) C. \( y=5 \sqrt{9+x^{2}} \) D. \( y=\
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• #58 plz :)
  57-58 Determine whether \( f^{\prime}(0) \) exists. 57. \( f(x)=\left\{\begin{array}{ll}x \sin \frac{1}{x} & \text { if } x \neq 0 \\ 0 & \text { if } x=0\end{array}\right. \) 58. \( f(x)=\left\{\begi
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• Resuelve la siguiente ecuación diferencial: (1−2/y+x)dy/dx+y=2/x−1
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  Given \( f(x, y)=-\left(x^{3} y+4 x y^{2}\right) \). Compute: \[ \frac{\partial^{2} f}{\partial x^{2}}= \] \[ \frac{\partial^{2} f}{\partial y^{2}}= \]
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  (1 point) Evaluate each function at the given point. \[ f(x, y, z)=\sqrt{6 x^{2}+7 y+3 z} \] \[ f(1,8,5)= \] \[ \begin{array}{l} f_{1}(x, y)=\frac{x}{y} \\ f_{1}(8,5)= \end{array} \] \[ f_{2}(y, x)=\f
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  If \( \ln (\sec \theta)=\frac{1}{2} \ln (10) \), find \( \sin \theta, \cos \theta \), and \( \tan \theta \)
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• Resuelve la siguiente ecuación diferencial: 3xdy/dx=2xe^x−3y+6x^2
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  4 pts) If \( f(x, y, z)=\sqrt{x-\arctan \left(e^{x z}\right)}+\sqrt{1+x y} \), find \( f_{x z y} \)
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  1) \( (6 \mathrm{pts}) \) If \( f(x, y)=5 x^{2}+y^{2} \), use differentials to approximate \( f(1.01,2.1) \).
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  3. Differentiate: \( y=\left(8 x^{2}+11 x-4\right)^{10} \quad 2 \) pts. 4. Differentiate: \( y=8 \tan 5 x+4 \cos 3 x+11 \sec x \quad 2 \) pts.
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  If \( x^{2}-x \cot y=y \), then \( y^{\prime}= \) A. \( \frac{2 x-\cot y}{1+x \csc ^{2} y} \) B. \( -\frac{2-\cot y}{\csc ^{2} y} \) C. \( \frac{2 x-\cot y}{1-x \csc ^{2} y} \) D. \( -\frac{2 x-\cot y
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  5. Differentiate: a) \( y=8 e^{4 x} \underline{2 \text { pts. }} \) b) \( y=\ln \left(5 x^{2}+7 x+4\right) \) c) \( y=\sin ^{-1}(3 x) 2 \) pts. d) \( y=\tan ^{-1}(7 x) 2 \) pts.
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  Solve the following Bernoulli differential equations: 1. \( y^{\prime}+y=x e^{x} \sqrt{y}, \quad y(0)=4 \) 2. \( \quad y^{\prime}-(\tan x) y=(\cos x) y^{4}, \quad y(0)=3 \)
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• find y'
  Differentiate the function. \[ y=(3 x-2)^{2}\left(2-x^{5}\right)^{3} \] \[ y^{\prime}= \]
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• 

  
  8. Maximize \[ p=x+2 y \] subject to \[ \begin{aligned} 30 x+20 y & \leq 600 \\ 0.1 x+0.4 y & \leq 4 \\ 0.2 x+0.3 y & \leq 4.5 \\ x \geq 0, y \geq 0 \end{aligned} \]
  2 answers

• 

  
  10. Minimize \[ c=0.4 x+0.1 y \] subject to \[ \begin{array}{llr} 30 x+20 y & \geq & 600 \\ 0.1 x+0.4 y & \geq & 4 \\ 0.2 x+0.3 y & \geq & 4.5 \\ x \geq 0, y \geq & 0 . \end{array} \]
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• ​​​​​​​
  Find all the second partial derivatives. \[ \begin{array}{c} f(x, y)=x^{8} y^{6}+2 x^{7} y \\ f_{x x}(x, y)=56 x^{6} y^{6}+84 x^{5} y \\ f_{x y}(x, y)=56 x^{7} y^{5}+14 x^{6} \\ f_{y x}(x, y)= \\ f_{y
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• 
  

  
  For the given DE: \( \left(1+y e^{x y}\right) d x+\left(2 y+x e^{x y}\right) d y=0 \), the \( \frac{\partial^{2} F}{\partial y \partial x}= \) \[ \begin{array}{l} 2+x^{2} e^{x y} \\ y^{2} e^{x y} \\ e
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  Find the equation of the tangent line to \( 3 x^{4}=4 y^{2}+6 x^{2} \) at \( (2,-\sqrt{6}) \). \[ \begin{array}{l} y=-9 x-18+\sqrt{6} \\ y=-\frac{3}{2} \sqrt{6} x+2 \sqrt{6} \\ y=-9 x-18-\sqrt{6} \\ y
  3 answers

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  If \( \ln (\sec \theta)=\frac{1}{2} \ln (10) \), find \( \sin \theta_{1} \cos \theta \), and \( \tan \theta \).
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  \( \lim _{x \rightarrow \infty} \frac{7 \cdot e^{x}}{7+5 e^{x}} \) \( y=\frac{7+x^{4}}{x^{2}-x^{4}} \)
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• Differentiate 3 y = ³√x³ + 12x + 2 • x³
  Differentiate. \[ y=\sqrt[3]{x^{3}+12 x+2} \cdot x^{3} \]
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  Match the functions with the graphs of their domains. 1. \( f(x, y)=\ln (3 x-y) \) 2. \( f(x, y)=3 x-y \) 3. \( f(x, y)=\sqrt{x^{3} y^{2}} \) 4. \( f(x, y)=e^{\frac{1}{3 x-y}} \)
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  Para \( d y-2 x y^{2} d x=0 \) las funciones son: \( g(x)=2 x, h(y)=y^{2} \) True False
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• Utilice la comprobación de "parciales mixtos" para ver si la siguiente ecuación diferencial es exacta. Si es exacto encontrar una función F(x,y) cuyo diferencial, dF(x,y) da la ecuación diferenci
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• Resuelve la siguiente ecuación diferencial: (1−2y+x)dydx+y=2x−1
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• Find fx, fy, and fz. f(x, y, z) = z(ln (xy))
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• #25 #29 #31 #33 #39 finding the derivative. Find the derivative of the following functions: 25, 29, 31, 33, 39
  25. \( y=e^{-x} \sin x \) 26. \( y=\sin x+4 e^{x} \) 27. \( y=x \sin x \) 28. \( y=e^{x}(\cos x+\sin x) \) 29. \( y=\frac{\cos x}{\sin x+1} \) 30. \( y=\frac{\frac{\sin x+\sin x}{1+\sin x}}{1+\cos x}
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• number 15
  11-16 Use the Chain Rule to find \( \partial z / \partial s \) and \( \partial z / \partial t \) 11. \( z=(x-y)^{5}, \quad x=s^{2} t, \quad y=s t^{2} \) 12. \( z=\tan ^{-1}\left(x^{2}+y^{2}\right), \q
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  #1. Compute the sum, if possible. If not possible, explain why. \[ \sum_{n=0}^{\infty} \frac{3-7^{n}}{14^{n}} \]
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  Find the partial derivatives of the function \[ f(x, y)=\frac{4 x-9 y}{5 x+2 y} \] \[ \begin{array}{l} f_{x}(x, y)= \\ f_{y}(x, y)= \end{array} \]
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• Find the derivative of following function 39, 42, 43, 47,
  35. \( y=w^{2} \sin w+2 w \cos w-2 \sin w \) 36. \( y=-x^{3} \cos x+3 x^{2} \sin x+6 x \cos x-6 \sin x \) 37. \( y=x \cos x \sin x \) 38. \( y=\frac{1}{2+\sin x} \) 39. \( y=\frac{\sin x}{1+\cos x} \)
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