Calculus Archive: Questions from April 12, 2023
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Find the first partial derivatives; \( f_{x} \& f_{y} \) of the function: \[ f(x, y, z)=\frac{\cos y}{x z^{2}} \] \[ f_{x}=\frac{\cos y}{z^{2}} ; f_{y}=\frac{\sin y}{x z^{2}} ; \quad f_{z}=\frac{2 \co2 answers -
Find all the second order partial derivatives of the given function. \[ f(x, y)=\ln \left(x^{2} y-x\right) \] \[ \begin{array}{l} f_{x x}(x, y)=\frac{2 x y-2 x^{2} y^{2}-1}{\left(x^{2} y-x\right)^{2}}2 answers -
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Evaluate \( \iiint_{W} f(x, y, z) d V \) for the function \( f \) and region \( \mathcal{W} \) specified: \[ f(x, y, z)=18(x+y) \quad W: y \leq z \leq x, 0 \leq y \leq x, 0 \leq x \leq 1 \] \[ \iiint_0 answers -
Evaluate \( \iiint_{B} f(x, y, z) d V \) for the specified function \( f \) and \( B \) : \[ f(x, y, z)=\frac{z}{x} \quad 2 \leq x \leq 6,0 \leq y \leq 4,0 \leq z \leq 8 \] \[ \iiint_{B} f(x, y, z) d2 answers -
find the general solution
17. \( \mathbf{y}^{\prime}=\frac{1}{6}\left[\begin{array}{rr}7 & 2 \\ -2 & 2\end{array}\right] \mathbf{y}, \quad \mathbf{y}(0)=\left[\begin{array}{l}0 \\ -3\end{array}\right] \)2 answers -
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17. \( \mathbf{y}^{\prime}=\frac{1}{6}\left[\begin{array}{rr}7 & 2 \\ -2 & 2\end{array}\right] \mathbf{y}, \quad \mathbf{y}(0)=\left[\begin{array}{l}0 \\ -3\end{array}\right] \)2 answers -
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La expresión \( \mathrm{s}(\mathrm{t})=\mathrm{t}^{3}-4.5 \mathrm{t}^{2}-7 \mathrm{t} \) es la función de la posición de una partícula. ¿Cuando alcanza la partícula una velocidad de \( 5 \mathrm2 answers -
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