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Calculus Archive: Questions from August 22, 2022

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  (1 point) Calculate \( \iint_{S} f(x, y, z) d S \) For \[ x^{2}+y^{2}=16, \quad 0 \leq z \leq 1 ; \quad f(x, y, z)=e^{-z} \] \[ \iint_{S} f(x, y, z) d S= \]
  2 answers
• Si f(x) = x sin x, entonces f'(π) es: a) π b) 1 c) 0 d)Ninguna de las anteriores
  1 answer
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  Evaluate the integral. \[ \int 6 \sin ^{2} x \cos ^{2} x d x \] \[ \int 6 \sin ^{2} x \cos ^{2} x d x= \]
  1 answer
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  Evaluate the integral. \[ \int \tan x \sec ^{2} x d x \] \[ \int \tan x \sec ^{2} x d x= \]
  3 answers

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  Find the expression for the function \( f \) when the differential equation is put into the form \( y^{(n)}=f\left(x, y, y^{\prime}, y^{\prime \prime}, \ldots, y^{(n-1)}\right) \) \( 1=x-3 \frac{d y}{
  1 answer
• Si f(x)=3 sin x cos x, evalúe f'(pi/3)
  Si \( f(x)=3 \sin x \cos x \), evalúe \( f^{\prime}\left(\frac{\pi}{3}\right) \) : \( -3 / 2 \) \( -1 / 2 \) \( -5 / 3 \) Ninguna de las anteriores
  3 answers

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  ZILLDIFFEQLA9 2.2.024. Encuentre una solución explícita del problema con valores iniciales dados. \[ \frac{d y}{d x}=\frac{y^{2}-1}{x^{2}-1}, \quad y(8)=8 \] \[ y= \]
  1 answer
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  I. Determine el limite, en caso de que no exista explique por qué. a) \( \lim _{(x, y) \rightarrow(0,1)} \frac{\arccos (x / y)}{1+x y} \) b) \( \lim _{(x, y) \rightarrow(0,0)} \frac{x-y}{\sqrt{x}+\sq
  3 answers
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  1. \( y=5 x^{2} \). Find \( \frac{\partial y}{\partial x} \) 2. \( y=12 x^{3}+3 z \). Find \( \frac{\partial y}{\partial x} \) and \( \frac{\partial y}{\partial z} \). 3. \( y=5 z^{2} \). Find \( \fra
  3 answers
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  Let \[ f(x, y)=\left\{\begin{array}{ll} \frac{x y\left(x^{2}-y^{2}\right)}{x^{2}+y^{2}} & , \quad(x, y) \neq(0,0) \\ 0 & , \quad(x, y)=(0,0) \end{array}\right. \] Compute \( f_{x y}(0,0) \) and \( f_{
  3 answers