Calculus Archive: Questions from May 31, 2023
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2.1. Determine the partial derivatives. 2.1.1. \( f(x, y)=3 x^{2}-x y+y \). 2.1.2. \( \rho(\phi, \theta)=\sin \phi \cos \theta \). 2.1.3. \( f(x, y)=e^{x-y}-e^{y-x} \). 2.1.4. \( g(x, y)=\frac{A x+B y2 answers -
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4.4
Calculate the double integral. \[ \iint_{R} \frac{3 x y^{2}}{x^{2}+1} d A, \quad R=\{(x, y) \mid 0 \leq x \leq 3,-2 \leq y \leq 2\} \]2 answers -
alculate all four second-order partial derivatives of \( f(x, y)=(5 x+4 y) e^{y} \). \[ \begin{array}{l} f_{x x}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \\ f_{y y}(x, y)= \end{array} \]2 answers -
Resuelve las siguientes ecuaciones diferenciales con condiciones iniciales Solve the following differential equations with initial conditions
\( \begin{array}{l}y^{\prime \prime}+4 y^{\prime}+4 y=(3+x) e^{-2 x}, \quad y(0)=2, y^{\prime}(0)=5 \\ y^{\prime \prime}+4 y^{\prime}+5 y=35 e^{-4 x}, \quad y(0)=-3, y^{\prime}(0)=1\end{array} \)2 answers -
Resuelve las siguientes ecuaciones diferenciales con condiciones iniciales Solve the following differential equations with initial conditions
\( \frac{d^{2} x}{d t^{2}}+\omega^{2} x=F_{0} \sin \omega t, \quad x(0)=0, x^{\prime}(0)=0 \) \( y^{\prime \prime}+4 y=g(x), \quad y(0)=1, y^{\prime}(0)=2 \)2 answers -
Evaluate the integral. \[ \int_{0}^{7} \int_{-\sqrt{49-x^{2}}}^{\sqrt{49-x^{2}}} \int_{-\sqrt{49-x^{2}-z^{2}}}^{\sqrt{49-x^{2}-z^{2}}} \frac{1}{\left(x^{2}+y^{2}+z^{2}\right)^{1 / 2}} d y d z d x= \]2 answers -
7. Find dy/dx: 10 y = tan¯¹ (2x(x + 1) ¹0)
Find \( d y / d x \) : \[ y=\tan ^{-1}\left(2 x(x+1)^{10}\right) \]2 answers -
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Given \( f(x, y)=-5 x^{5}-x y^{3}+6 y^{2} \), find the following numerical values: \[ f_{x}(1,4)= \] \[ f_{y}(1,4)= \]2 answers -
3. Find all horizontal asymptotes of the following function. \[ f(x)=\left\{\begin{array}{ll} \frac{3 x-1}{\sqrt{3 x^{2}+2}}, & \text { if } x \leq 2 \\ \frac{7 e^{6 x}-2 e^{3 x}+2}{2 e^{6 x}+3 e^{3 x2 answers -
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\( \begin{array}{c}F(x, y, z)=x^{2} y^{2} \underline{l}+\tan ^{-1}\left(\frac{x}{y}\right) \underline{\jmath}+\sin \left(\frac{x}{y}\right) \underline{k} \\ \\ \text { find } \nabla^{\circ} F(x, y, z)2 answers -
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Find dy/dx for y =1/15 (3x-1)^5+ (4-(1/2x^2))^-1
\( y=\frac{1}{15}(3 x-1)^{5}+\left(4-\frac{1}{2 x^{2}}\right)^{-1} \)2 answers -
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Find all the first and second order partial derivatives of \( f(x, y)=3 \sin (2 x+y)-\cos (x-y) \). A. \( \frac{\partial f}{\partial x}=f_{x}=6 \cos (2 x+y)+\sin (x-y) \) B. \( \frac{\partial f}{\part2 answers -
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Realiza el procedimiento que te permita seleccionar en forma correcta la opción que contenga la solución particular de la siguiente ecuación diferencial \[ y^{\prime \prime}+y^{\prime}+3 y=\operato2 answers -
Find all the second partial derivatives \[ f(x, y)=x^{5} y^{7}+2 x^{6} y \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y)= \]2 answers -
I.- Resuelva las siguientes ecuaciones diferenciales usando el método de coeficientes indeterminados. \[ y^{\prime \prime \prime}-2 y^{\prime \prime}-4 y^{\prime}+8 y=6 x e^{2 x} \]2 answers -
Evaluate \( \iiint_{\mathcal{B}} f(x, y, z) d V \) for the specified function \( f \) and \( \mathcal{B} \) : \[ \iiint_{\mathcal{B}} f(x, y, z) d V=f(x, y, z)=\frac{z}{x} \quad 2 \leq x \leq 4,0 \leq2 answers -
I.- Resuelva las siguientes ecuaciones diferenciales usando el método de coeficientes indeterminados. \[ y^{\prime \prime \prime}-y^{\prime \prime \prime}-4 y^{\prime}+4 y=5-e^{x}+e^{2 x} \]2 answers