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Calculus Archive: Questions from October 04, 2022

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  Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ \begin{array}{l} y=\frac{\ln (5 x)}{x^{3}} \\ y^{\prime}= \end{array} \]
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  L. Find \( y^{\prime} \) 1.) \( y=\cos \left(x^{2}+9\right) \)
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  \( y=\cot ^{4}\left(4-x^{2}\right) \) \( 8 x \csc ^{\wedge} 2\left(4 x^{\wedge} 2\right) \cot ^{\wedge} 3\left(4 x^{\wedge} 2\right) \) \( 8 x \csc ^{\wedge} 2\left(4 x^{\wedge} 2\right) \sec ^{\wedge
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  Evaluate the double integral. \[ \iint_{D} 7 x \sqrt{y^{2}-x^{2}} d A, D=\{(x, y) \mid 0 \leq y \leq 3,0 \leq x \leq y\} \]
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  8) Resolver la EDO \( \frac{d y}{d x}-2 x y=x^{3} e^{-x^{2}} \), con \( y(0)=1 \) R: Esta es una propuesta de solución, \( y=-\frac{1}{4}\left(x^{2}+\frac{1}{2}\right) e^{-x^{2}}+\frac{9}{8} e^{x^{2}
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• i want answers for 23,27,28,30
  22-35 Find the derivative of the function. Simplify where possible. 22. \( y=\tan ^{-1}\left(x^{2}\right) \) 23. \( y=\left(\tan ^{-1} x\right)^{2} \) 24. \( g(x)=\arccos \sqrt{x} \) 25. \( y=\sin ^{-
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  \[ y=\tan \left(x^{3}+3 x^{2}+6 x\right) \] \( y=e^{\sin (x)-\cot (x)} \), find \( y^{\prime} \)
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• PLEASE HELP WITH 9.22 9.26 9.30
  Solve the following differential equations. 9.17. \( y^{\prime \prime}-y=0 \) 9.18. \( y^{\prime \prime}-y^{\prime}-30 y=0 \) 9.19. \( y^{\prime \prime}-2 y^{\prime}+y=0 \) 9.21. \( y^{\prime \prime}+
  2 answers
• #3 please
  Find the following derivatives 1. \( y=x^{2}(5 x-1)^{3} \) 2. \( y=4 x^{2}\left(3 x^{2}+2 x+1\right)^{3} \) 3. \( y=\frac{(3 x+2)^{7}}{x-1} \)
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  Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ \begin{array}{c} y=\frac{\ln (5 x)}{x^{3}} \\ y^{\prime}=\frac{1-3 \ln 5-3 \ln x}{x^{4}} \end{array} \]
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• consider the following graph of f(x) and find f(0)f(1) f(2) f(-2) and the domain of f(x)
  II. Considere la siguiente gráfica de \( f(x) \) : Halle: 1. \( f(2) \) 2. \( f(-2) \) 3. \( f(0) \) 4. \( f(1) \) 5. Dominio de \( f(x) \)
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  Integrate the function. \[ \begin{array}{l} \int \frac{x^{3}}{\sqrt{x^{2}+8}} d x \\ \frac{1}{3}\left(x^{2}+8\right)^{3 / 2}-8 \sqrt{x^{2}+8}+C \\ \frac{1}{8}\left(x^{2}+8\right)^{3 / 2}-\sqrt{x^{2}+8
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  7. Differentiate the following functions using derivative rules: (a) \( y=x^{2}+3 x+5 x^{4 / 5}+1 \) (b) \( y=e^{x}(\sin x) \) (c) \( y=\frac{4 x^{3}+2 x+3}{\sqrt{x}} \) (d) \( y=(\tan x)^{3 / 2} \)
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• Encuentra la ecuación del plano tangente a la superficie: at the point (1,0,-1)
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  2. Solve \[ y^{\prime}(x)+4(x)=y^{2}(x)(\cos x-\sin x) \]
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  Find the first partial derivatives of the function. \[ \begin{array}{l} h(x, y, z, t)=x^{8} y \cos \left(\frac{z}{t}\right) \\ h_{x}(x, y, z, t)= \\ h_{y}(x, y, z, t)= \\ h_{z}(x, y, z, t)= \\ h_{t}(x
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  Differentiate the function. \[ \begin{array}{c} y=\ln \left(\left|3+t-t^{3}\right|\right) \\ y^{\prime}=\frac{\left(1-3 t^{3}\right)\left(3+t-t^{3}\right)}{\left|t^{6}-2 t^{4}-6 t^{3}+t^{2}+6 t+9\righ
  2 answers

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  Explique si la siguiente integral se puede resolver con las fórmulas y técnicas de integración estudiadas: \[ \int_{2}^{3} \frac{2 x-3}{\sqrt{4 x-x^{2}}} d x \]
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• Explain if the following integral can be solved with the formulas and integration techniques studied.
  Explique si la siguiente integral se puede resolver con las fórmulas y técnicas de integración estudiadas. \[ \int_{2}^{3} \frac{2 x-3}{\sqrt{4 x-x^{2}}} d x \]
  2 answers

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  (1 point) Let \( f(x, y, z)=\frac{x^{2}-3 y^{2}}{y^{2}+3 z^{2}} \). Then \[ \begin{array}{l} f_{x}(x, y, z)= \\ f_{y}(x, y, z)= \\ f_{z}(x, y, z)= \end{array} \]
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  (1 point) Let \( f(x, y, z)=\frac{x^{2}-5 y^{2}}{y^{2}+5 z^{2}} \). Then \[ \begin{array}{l} f_{x}(x, y, z)= \\ f_{y}(x, y, z)= \\ f_{z}(x, y, z)= \end{array} \]
  2 answers
• plz answer asap
  Let \( f \) and \( g \) be functions that satisfy \( f(4)=-1, g(4)=3, f^{\prime}(4)=2 \), and \( g^{\prime}(4)=-3 \). Find \( h^{\prime}(4) f \) for \( h(x)=f(x) g(x)-2 f(x)+7 \). A. \( -6 \) B. 5 C.
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  Compute the gradient for the following functions: (a) \( f(x, y)=x^{2} y^{5} \). (b) \( g(x, y)=x^{2} \sin \left(x+y^{4}\right) \). (c) \[ h(x, y, z)=\frac{2 x+2 y+2 z}{\sqrt{x^{2}+y^{2}+z^{2}}} . \]
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• Find dy/dx
  Differentiate.
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  (1 point) Let \( f(x, y, z)=\frac{x^{2}-4 y^{2}}{y^{2}+4 z^{2}} \). Then \[ \begin{array}{l} f_{x}(x, y, z)= \\ f_{y}(x, y, z)= \\ f_{z}(x, y, z)= \end{array} \]
  2 answers
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  If \( f(x)=\frac{4 x^{2} \tan x}{\sec x} \), find \[ f^{\prime}(x)=\frac{4 x(x+2 \tan (x))}{\sec (x)} \] Find \( f^{\prime}(3) \)
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  Evaluate the double integral. \[ \iint_{D} \frac{y}{x^{2}+1} d A, \quad D=\{(x, y) \mid 0 \leq x \leq 9,0 \leq y \leq \sqrt{x}\} \]
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  7. Find the following indefinite integrals (show steps): (a) \( \int\left(3 x^{3}+\frac{5+x^{4}}{x^{2}}\right) d x \) (b) \( \int \frac{5+2 \sin x}{\cos ^{2} x} d x \)
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• Solve the following initial value problem. dy dx  =  y2 − 12y + 35, y(0)  =  2
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• #13
  13-14 Find \( \int_{0}^{2} f(x, y) d x \) and \( \int_{0}^{3} f(x, y) d y \) 13. \( f(x, y)=x+3 x^{2} y^{2} \) 14. \( f(x, y)=y \sqrt{x+2} \)
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• Help!
  (1 point) Let \( f(x, y, z)=\frac{x^{2}-6 y^{2}}{y^{2}+3 z^{2}} \). Then \[ \begin{array}{l} f_{x}(x, y, z)= \\ f_{y}(x, y, z)= \\ f_{z}(x, y, z) \end{array} \]
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  \( y=e^{3 x^{2}}(4 x-1)^{5} \)
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• do 60
  Sketching Level Surfaces In Exercises 53-60, sketch a typical level surface for the function. 53. \( f(x, y, z)=x^{2}+y^{2}+z^{2} \) 54. \( f(x, y, z)=\ln \left(x^{2}+y^{2}+z^{2}\right) \) 55. \( f(x,
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  (1 point) Let \( f(x, y, z)=\frac{x^{2}-2 y^{2}}{y^{2}+3 z^{2}} \). Then \( f_{x}(x, y, z)= \) \[ f_{y}(x, y, z)= \] \[ f_{z}(x, y, z)= \]
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  \( y=\frac{3 x^{6}-9 x^{5}+2}{x^{3}} \)
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  Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For \[ y=9-z^{2}, \quad 0 \leq x, z \leq 9 ; \quad f(x, y, z)=z \] \[ \iint_{\mathcal{S}} f(x, y, z) d S= \]
  1 answer
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  12. \( \lim _{(x, y) \rightarrow(\pi / 2,0)} \frac{\cos y+1}{y-\sin x} \)
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  Find \( y^{\prime} \) and \( y^{\prime \prime} \) \[ y=\sqrt{x} \ln (x) \] \[ y^{\prime}= \]
  2 answers
• please help #18,22,26,42 find the derivative of the function using the right rule
  17. \( y=x^{2} e^{-3 x} \) 18. \( f(t)=t \sin \pi t \) 19. \( f(t)=e^{a t} \sin b t \) 20. \( A(r)=\sqrt{r} \cdot e^{r^{2}+1} \) 21. \( F(x)=(4 x+5)^{3}\left(x^{2}-2 x+5\right)^{4} \) 22. \( G(z)=(1-4
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• Use the double integral to check that the moments of inertia in the region about the axes are as illustrated in the figure. then calculate the radii of gyration about each axis
  I. Utilice la integral doble para comprobar que los momentos de inercia en la región con respecto a los ejes son los que se ilustran en la figura. Luego calcule los radios de giro con respecto a cada
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  5. \( f(x, y)=x^{3}+3 x^{2} y+3 x y^{2}+y^{3} \) a. \( f_{x}(x, y)= \) b. \( f_{y}(x, y)= \)
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  \[ f(x, y)=\ln \left(1+x^{2} y^{2}\right) \] a. \( f_{x}(x, y)= \) b. \( f_{y}(x, y)= \)
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  \[ f(x, y)=e^{x^{2}+y^{2}} \] a. \( f_{x}(x, y)= \) b. \( f_{y}(x, y)= \)
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  (1 point) Find the partial derivatives of the function \[ \begin{array}{l} f_{x}(x, y) \\ f_{y}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \end{array} \] \[ f(x, y)=x y e^{5 y} \]
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  Given \( f(x, y)=-\left(3 x^{3} y+x y^{5}\right) \). Compute: \[ \frac{\partial^{2} f}{\partial x^{2}}= \] \[ \frac{\partial^{2} f}{\partial y^{2}}= \]
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  Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-5 y^{\prime \prime}-y^{\prime}+5 y=0 \] \[ \begin{array}{l} y(0)=-3, \quad y^{\prime}(0)=4, \quad y^{\prime \prime}(0)=93 \\ y(x)=
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  If \( f(x)=\frac{7 x^{2}+4 x+2}{\sqrt{x}} \), , then: \[ f^{\prime}(x) \] \( f^{\prime}(4) \)
  2 answers