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Calculus Archive: Questions from August 19, 2022

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  Given \( f(x, y)=5 e^{4 x} \sin (4 y) \) \[ \nabla f(0, \pi)= \]
  3 answers

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  (3) \( \int_{0}^{\pi / 2} \int_{0}^{\sin y} e^{x} \cos y d x d y=e-2 \) (4) \( \int_{1}^{e} \int_{0}^{1 / 2} \int_{0}^{\sqrt{1-x^{2}}} \frac{d y d x d z}{1-x^{2}}=\frac{\pi}{6}(0-1) \) (5) \( \int_{0}
  3 answers

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  Determine the domain of the function \[ f(x, y)=3 \ln \left(2 x+y^{2}+5\right) \] \[ \operatorname{dom}(f)=\left\{(x, y) \in \mathbb{R}^{2}: x \leq \frac{y^{2}+5}{2}\right\} \] \[ \begin{array}{l} \op
  1 answer

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  [-/25 Points] ZILLDIFFEQLA9 1.1.013. "sen \( (x) \) " se escribe como "sin(x)".) \[ y^{\prime \prime}-8 y^{\prime}+25 y=0 ; \quad y=e^{4 x} \cos 3 x \] Cuando \( y=e^{4 x} \cos 3 x \), \[ y^{\prime}=
  3 answers

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  9. If \( y=\cot ^{-1}\left(\log _{3} 2 x^{2}\right) \) then \( \frac{d y}{d x}= \) : A) \( \frac{2}{x \ln 3} \) B) \( \frac{-2}{x\left(1+4 x^{4}\right) \ln 3} \) C) \( \frac{-2}{x\left(1+4 x^{4}\right
  3 answers

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  Solve the following systems of ODE's. 1. \( \left\{\begin{array}{l}x^{\prime}=-4 x+6 y \\ y^{\prime}=-3 x+5 y\end{array}\right. \) 2. \( \left\{\begin{array}{l}x^{\prime}=x-y \\ y^{\prime}=5 x-3 y\end
  3 answers

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  Solve the following ODE's using variation of parameters 1. \( y^{\prime \prime}-2 y^{\prime}+y=\frac{e^{x}}{x^{5}} \) 2. \( y^{\prime \prime}+y=\sec (x) \)
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  Evaluate the indefinite integral \[ \int(11 \sin x+13 \tan x) d x \]
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  If \( f(x, y)=\frac{x^{2} y}{\left(3 x-y^{2}\right)} \), find the following. (a) \( f(1,5) \) (b) \( f(-3,-1) \) (c) \( f(x+h, y) \) (d) \( f(x, x) \)
  3 answers

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  use el método de Euler para obtener una aproximación a cuatro decimales del valor indicado, ejecute a mano la ecuación de recursión \[ y_{n+1}=y_{n}+h f\left(x_{n}, y_{n}\right) \] usando primero
  1 answer

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  Use el método de Euler para obtener una aproximación a cuatro decimales del valor indicado, ejecute a mano la ecuación de recursión (3) en la sección \( 2.6 \) \[ y_{n+1}=y_{n}+h f\left(x_{n^{\pr
  2 answers

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  \( \frac{d y}{d x}-a^{-0.01 x y^{2}} \)
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  \[ \frac{d y}{d x}=x^{2}-y^{2} \] (a) \( y(-2)=1 \) \( y(3)=0 \) \( y(0)=0 \)
  1 answer

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  Given \( f(x, y)=5 e^{2 x} \sin (2 y) \) \[ \nabla f\left(0, \frac{\pi}{2}\right)= \]
  3 answers