Calculus Archive: Questions from December 17, 2023
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Find all the first and second order partial derivatives of \( f(x, y)=-5 \sin (2 x+y)-10 \cos (x-y) \). A. \( \frac{\partial f}{\partial x}=f_{x}= \) B. \( \frac{\partial f}{\partial y}=f_{y}= \) C. \1 answer -
Given \( f(x, y)=8 x y^{3}-8 x^{6} y \). Compute: \[ \begin{array}{l} \frac{\partial^{2} f}{\partial x^{2}}= \\ \frac{\partial^{2} f}{\partial y^{2}}= \end{array} \]1 answer -
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\( \begin{array}{l}y^{\prime \prime}+3 y^{\prime}+2 y=\sinh x \\ y^{\prime \prime}+y=\cos x \\ y^{\prime \prime}+4 y=\sin 2 x\end{array} \)1 answer -
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( int_{0}^{32} int_{x}^{sqrt{64 x-x^{2}}} 9 sqrt{x^{2}+y^{2}} d y d x= )
\( \int_{0}^{32} \int_{x}^{\sqrt{64 x-x^{2}}} 9 \sqrt{x^{2}+y^{2}} d y d x= \)1 answer -
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Reusleve estos problema por favor
1- Calcular la longitud de arco de la parábola semicubica f: \( 5 y^{3}=x^{2} \) comprendido dentro de la circunferencia \[ \text { g: } x^{2}+y^{2}=6 \] (4 puntos) 2- La base de un cilindro recto es1 answer -
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Situacion 1: Describa la derivada direccional de la función \( f \) en la dirección de \( \vec{u}=\cos \theta i+\sin \theta j \) cuando (a) \( \theta \) \( =0^{0} y(b) \theta=90^{0} \). Situación 21 answer -
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26. Find the horizontal asymptote(s) of the function \[ f(x)=\frac{e^{8 x}+10}{5-3 e^{8 x}} \] (a) \( y=-\frac{1}{3} \) only (b) \( y=-\frac{1}{3}, y=5 \) (c) \( y=-\frac{1}{3}, y=2 \) (d) \( y=2, y=51 answer -
(d) Let \( \mathbf{F}(x, y, z)=x \mathbf{i}+y \mathbf{j}+z \mathbf{k} \) and let \( f(x, y, z)=|\mathbf{F}(x, y, z)| \). Show that: i. \( \nabla \times \mathbf{F}=\mathbf{0} \). ii. \( \nabla f=\mathb1 answer -
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17) (a) Find the general solution. (i) \( y^{\prime}=\left(x^{2}+1\right) y \). (ii) \( y^{\prime}=y^{2}-y \). (b) Solve the initial value problem. (i) \( y^{\prime}=\frac{x-1}{y^{2}}, y(0)=2 \). (ii)1 answer