Calculus Archive: Questions from October 27, 2022
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Find \( y^{\prime} \) and \( y^{\prime \prime} \), \[ y=\cos (\sin (2 \theta)) \] \[ y^{\prime}= \] \[ y^{*}= \] If \( F(x)=f(g(x)) \), where \( f(-4)=4, f^{\prime}(-4)=7, f^{\prime}(5)=2, g(5)=-4 \)3 answers -
Find \( y^{\prime} \) and \( y^{\prime \prime} \), \[ \begin{array}{l} y=\cos (\sin (2 \theta)) \\ y^{\prime}= \\ y^{\prime}=-4 \cos (\sin (2 \theta) \cdot \cos (2 \theta)+4 \sin (2 \theta) \sin (\sin2 answers -
\[ \begin{array}{c} \star \frac{1}{\cos x}=? \\ \star f(x)=\sin ^{3} x \end{array} \] differentiabte \( { }^{\prime} y(x)= \) ?2 answers -
i need only 76 find second derivative
Find \( y^{\prime \prime} \) in Exercises 71-78. 71. \( y=\left(1+\frac{1}{x}\right)^{3} \) 72. \( y=(1-\sqrt{x})^{-1} \) 73. \( y=\frac{1}{9} \cot (3 x-1) \) 74. \( y=9 \tan \left(\frac{x}{3}\right)2 answers -
\( \nabla \cdot(\nabla \times \mathbf{F}) \), if \( \mathbf{F}(x, y, z)=3 e^{x z} \mathbf{i}+9 x e^{y} \mathbf{j}-9 e^{y z} \mathbf{k} \) \[ \nabla \cdot(\nabla \times \mathbf{F})= \]2 answers -
Find \[ \left.\frac{d^{2} y}{d \theta^{2}}\right|_{\theta=\frac{\pi}{4}} \] , if \[ y=\sec \theta \]2 answers -
Let \( Q(x, y) \) be the statement " \( x+y=x-y^{\prime} \). If the domain for both variables consists of all integers, what are the truth values? (a) \( Q(1,1) \) (b) \( Q(2,0) \) (c) \( \forall y Q(2 answers -
Evaluate the triple integral \( \iiint_{E} f(x, y, z) d V \) over the solid \( E \). \[ f(x, y, z)=x^{2}+y^{2}, E=\left\{(x, y, z) \mid x^{2}+y^{2} \leq 4, x \geq 0, x \leq y, 0 \leq z \leq 5\right\}2 answers -
valuate the triple integral \( \iiint_{B} f(x, y, z) d V \) over the solid \( B \). \[ f(x, y, z)=1-\sqrt{x^{2}+y^{2}+z^{2}}, B=\left\{(x, y, z) \mid x^{2}+y^{2}+z^{2} \leq 16, y \geq 0, z \geq 0\righ2 answers -
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show all steps.
For \( f(x, y, z)=x^{2} y-z \) and \( \vec{F}(x, y, z)=x \hat{\imath}-x y \hat{\jmath}+z^{2} \hat{k} \) calculate \( \nabla f+\nabla \times F \).2 answers -
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Find .... for the following function
3. Hallar \( \frac{\partial}{\partial x}\left(\frac{\partial f}{\partial y}\right)=\frac{\partial^{2} f}{\partial x y} \) y \( \frac{\partial}{\partial \dot{y}}\left(\frac{\partial f}{\partial x}\righ2 answers -
For \( f(x, y, z)=x^{2} y-z \) and \( \vec{F}(x, y, z)=x \hat{\imath}-x y \hat{\jmath}+z^{2} \hat{k} \) calculate \( \nabla f+\nabla \times F \).2 answers -
Usinf the chain law find ...
4. Usando la regla de la cadena apropiada hallar \( \frac{\partial w}{\partial s} \) y \( \frac{\partial w}{\partial t} \) a. \( w=x \cos (y z), x=s^{2}, y=t^{2}, \quad z=s-2 t \).2 answers -
Find a function f ...
6. Hallar una función \( f \) tal que \( \nabla f=2 x y \mathbf{i}+\left(x^{2}+z^{2}\right) \mathbf{j}+2 y z \mathbf{k} \)2 answers -
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For \( f(x, y, z)=x^{2} y-z \) and \( \vec{F}(x, y, z)=x \hat{\imath}-x y \hat{\jmath}+z^{2} \hat{k} \) calculate \( \nabla f+\nabla \times F \).2 answers -
Sistemas de ED de primer orden
\( \mathbf{x}^{\prime}=\left(\begin{array}{ll}3 & -2 \\ 2 & -2\end{array}\right) \mathbf{x} \)2 answers -
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Find the derivative of the function. \[ y=6^{\sin (\pi x)} \] \[ y^{\prime}= \] Need Help? Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ y=\cos \left(x^{2}\right) \] \[ y^{\prime}= \] \[ y^{\p3 answers -
Surface Area of Revolution: Set up and evaluate the definite integral over the area of the surface created by revolving the curve about the x-axis:
Resuelva: Área de Superficie de Revolución Establezca y evalúe la integral definida por el área de la superficie creada al hacer girar la curva sobre el eje de \( x \) : 37. \( y=\frac{1}{3} x^{3}2 answers -
only 19 and 22
1. \( y=\ln 5 x \) 2. \( y=\ln \frac{x}{3} \) 3. \( y=\ln |1+x| \) 4. \( y=\ln (2+\sqrt{x}) \) 5. \( y=\ln \left|x^{2}-1\right| \) 6. \( y=\ln \left|x^{3}-7 x^{2}-3\right| \) 7. \( y=\ln \left(\frac{x2 answers -
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\( \iint_{R} \frac{x y}{1+x^{4}} d A, \quad R=\{(x, y) \mid-1 \leqslant x \leqslant 1,0 \leqslant y \leqslant 1\} \) \[ \iint_{R}\left(1+x^{2} \sin y+y^{2} \sin x\right) d A, \quad R=[-\pi, \pi] \time2 answers -
29. \( \iint_{R} \frac{x y^{2}}{x^{2}+1} d A, \quad R=\{(x, y) \mid 0 \leqslant x \leqslant 1,-3 \leqslant y \leqslant 3\} \)2 answers -
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#55 #56 #65 #66 Thank you!! <3
In Exercises 51-70, find \( d y / d t \). 51. \( y=\sin ^{2}(\pi t-2) \) 52. \( y=\sec ^{2} \pi t \) 53. \( y=(1+\cos 2 t)^{-4} \) 54. \( y=(1+\cot (t / 2))^{-2} \) 55. \( y=(t \tan t)^{10} \) 56. \(2 answers -
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(1 point) Calculate all four second-order partial derivatives of \( f(x, y)=4 x^{2} y+3 x y^{3} \). \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y)= \] (1 point) Calcu2 answers -
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Compute the partial derivative: \[ f(x, y)=\sin \left(x^{7}-5 y\right) \] \[ f_{y}(0, \pi)= \] Given \( f(x, y)=8 x y^{6}-5 x^{4} y \) \[ \frac{\partial^{2} f}{\partial x^{2}}= \] \[ \frac{\partial^{2 answers -
Express the integral \( \iiint_{E} f(x, y, z) d V \) as an iterated integral in six different ways, where \( \mathrm{E} \) is the solid bounded by \( z=0, z=2 y \) and \( x^{2}=25-y \). 1. \( \int_{a}2 answers -
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(1 point) Calculate all four second-order partial derivatives of \( f(x, y)=(5 x+4 y) e^{y} \). \( f_{x x}(x \), \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y) \]2 answers -
1. Solve the initial value problem. \[ 4 y^{\prime \prime}-4 y^{\prime}+y=0, \quad y(0)=2, \quad y^{\prime}(0)=-\frac{1}{5} \]2 answers -
2) Find \( \frac{d y}{d x} \) for each. Simplify. a) \( y=\frac{e^{3 x}}{x^{6}} \) b) \( y=\left(e^{5 x}+2\right)^{4} \)2 answers -
Help Entering Answers (1 point) Evaluate the double integral \( \iint_{R} 8 \sin (3 x-y) d A= \) where \( R=\{(x, y) \mid 0 \leq x \leq \pi / 2,0 \leq y \leq \pi / 2\} \)2 answers -
If \( 17+9 f(x)+8 x^{2}(f(x))^{3}=0 \) and \( f(-1)=-1 \), find \( f^{\prime}(-1) \) \[ f^{\prime}(-1)= \]2 answers -
9. Differentiate: (a) \( y=\frac{\sin x}{1+\tan x} \). (b) \( F(x)=\sqrt{1-2 x} \) (c) \( y=10^{1-x^{2}} \) (d) \( y=\cos \left(\frac{1-e^{2 x}}{1+e^{2 x}}\right) \) (e) \( f(t)=\tan \left(e^{t}\right1 answer -
Sistemas de ED de primer orden
\( \mathbf{x}^{\prime}=\left(\begin{array}{ll}3 & -4 \\ 1 & -1\end{array}\right) \mathbf{x} \)2 answers -
Sistemas de ED de primer orden
\( \mathbf{x}^{\prime}=\left(\begin{array}{ll}3 & -2 \\ 4 & -1\end{array}\right) \mathbf{x} \)2 answers -
4) Para la serie de potencias \( \sum_{n=0}^{\infty} \frac{(x-2)^{n+1}}{(n+1) 4^{n+1}} \), halla el intervalo de convergencia. a) \( (-2,6) \) b) \( [-2,6] \) c) \( (-2,6] \) d) \( [-2,6) \) e) Ningun2 answers -
1. Identifique la gráfica en el espacio \( \frac{x^{2}}{4}-\frac{y^{2}}{25}-\frac{z^{2}}{49}=1 \) a. Hiperboloide de un manto paralelo al eje " \( x \) " b. Hiperboloide de dos mantos paralelo al eje2 answers -
Calcular el trabajo realizado al mover una particula desde \( P(0,0,0) \) hasta el punto \( Q(4,7,5) \). Si la magnitud y dirección de la fuerza están dados por \( \vec{v}=\langle 1,4,8\rangle \). L2 answers -
Find the Jacobian of the transformation. \[ x=u^{4} / v^{5}, y=v^{5} / w^{5}, z=w^{5} / u^{4} \] \[ \frac{\partial(x, y, z)}{\partial(u, v, w)}= \]2 answers -
can somebody please help with the second part to this question?
Resuelva: 1. Encuentre la ecuación del plano determinado por los puntos \( \mathrm{P}(1,2,3) \) \[ Q(2,3,1) R(0,-2,-1) \] 2. Encuentre las ecuaciones paramétricas y simétricas para la linea que pas2 answers -
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Let \( f(x, y)=x^{2}+y^{2} \) 1. Find all extrema or saddle points. 2. Maximize \( f(x, y) \) on \( x^{4}+y^{4} \leq 2 \)2 answers -
Find \( \sin \left(\frac{x}{2}\right), \cos \left(\frac{x}{2}\right) \), and \( \tan \left(\frac{x}{2}\right) \) from the given information. \[ \begin{array}{l} \cot (x)=8,180^{\circ}2 answers