Calculus Archive: Questions from March 07, 2023
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please solve 13,16,17 only
13-18 Show that the limit does not exist. 13. \( \lim _{(x, y) \rightarrow(0,0)} \frac{y^{2}}{x^{2}+y^{2}} \) 14. \( \lim _{(x, y) \rightarrow(0,0)} \frac{2 x y}{x^{2}+3 y^{2}} \) 15. \( \lim _{(x, y)2 answers -
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Evaluate the integral. \[ \int 12 \sin ^{2} x \cos ^{2} x d x \] \[ \int 12 \sin ^{2} x \cos ^{2} x d x= \]2 answers -
Which of the following linear approximation of \( f(x, y) \) at the point \( \left(x_{0}, y_{0}, z_{0}\right) \) ? \[ \begin{array}{l} L(x, y)=f_{x}\left(x_{0}, y_{0}\right)\left(x+x_{0}\right)+f_{y}\2 answers -
Find the indicated partial derivative (a) \( f(x, y, z)=e^{x y z^{2}} \quad f_{y z z} \) b) \( f(x, y, z)=\frac{x^{2}}{x^{3}-y^{2}+x y z} \quad \frac{\partial^{3} f}{\partial z^{2} \partial y} \)2 answers -
please i need help with question number #1,3,5,9,11, &17
1-16 Differentiate. 1. \( f(x)=x^{2} \sin x \) 2. \( f(x)=x \cos x+2 \tan x \) 3. \( f(x)=3 \cot x-2 \cos x \) 4. \( y=2 \sec x-\csc x \) 5. \( y=\sec \theta \tan \theta \) 6. \( g(t)=4 \sec t+\tan t2 answers -
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Which of the following linear approximation of \( f(x, y) \) at the point \( \left(x_{0}, y_{0}, z_{0}\right) \) ? \[ \begin{array}{l} L(x, y)=f_{x}\left(x_{0}, y_{0}\right)+f_{y}\left(x_{0}, y_{0}\ri2 answers -
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pleaseee
Find the values of the function. \[ g(x, y)=x^{2} e^{2 y} \] (a) \( g(-2,0) \) (b) \( g\left(2, \frac{1}{2}\right) \) (c) \( g(1,-1) \) (d) \( g(-4, y) \) Find the values of the function. \[ f(x, y)=2 answers -
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Given \( f(x, y)=2 x y^{4}-7 x^{2} y \) \[ \frac{\partial^{2} f}{\partial x^{2}}= \] \[ \frac{\partial^{2} f}{\partial y^{2}}= \]2 answers -
I. Determine la longitud del arco en el intervalo dado a) \( r(t)=i+t^{2} j+t^{3} k \) b) \( r(t)=\langle 4 t,-\cos t, \operatorname{sen} t\rangle ;\left[0, \frac{3 \pi}{2}\right] \) II. Determine e i2 answers -
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Solve \[ \begin{array}{l} x-y+z-w=2 \\ y+2 z+w=2 \\ -z+w=3 \\ -x+2 y-3 z+5 w=1 \\ x=\quad, y=\quad, z=\quad, w= \\ \end{array} \]2 answers -
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II. Determine e interprete la curvatura K de la curva en el valor del parámetro dado a) \( r(t)=t^{2} i+j ; t=2 \) b) \( r(t)=\left\langle 3 t, 2 t^{2}\right\rangle \) en el punto \( (-3,2) \) c) \(2 answers -
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1. Find the absolute extreme values of the function \( f(x, y)=3 x^{2}-3 x y+y^{3} \) on the rectangle \( D=\{(x, y): 0 \leq x \leq 2,0 \leq y \leq 1\} \).2 answers -
Which of the following linear approximation of \( f(x, y) \) at the point \( \left(x_{0}, y_{0}, z_{0}\right) \) ? \[ \begin{array}{l} L(x, y)=f_{x}\left(x_{0}, y_{0}\right)\left(x-x_{0}\right)+f_{y}\2 answers -
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Compute the gradient vector fields of the following functions: A. \( f(x, y)=6 x^{2}+2 y^{2} \) \( \nabla f(x, y)=\quad \mathbf{i}+\quad \mathbf{j} \) B. \( f(x, y)=x^{1} y^{9} \) \( \nabla f(x, y)=\q2 answers -
Find y ′ and y ″ by implicit differentiation. cos(y) + sin(x) = 1 y ' = y '' =
Find \( y^{\prime} \) and \( y^{\prime \prime} \) by implicit differentiation. \[ \cos (y)+\sin (x)=1 \] \[ y^{\prime}= \] \[ y^{\prime \prime}= \]3 answers -
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Compute \( y^{\prime} \) for the equation \( x y+1=y^{5} \) (a) \( y^{\prime}=\frac{y^{5}-1}{x} \) (b) \( y^{\prime}=0 \) (c) \( y^{\prime}=\frac{5 y^{4}}{x} \) (d) \( y^{\prime}=-\frac{y}{x-5 y^{4}}2 answers -
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Calculate the volume using washer's method
Son \( R \) la reion del plamo limitada por la neta \( y-2 x=0 \) y la pardbola \( x^{2}-y=0 \) Utilice d metodo de Arandelas pura calcular d twiumen del solido obterido al notar \( R \) alrefodor de2 answers -
Find y'' please.
Find \( y^{\prime} \) and \( y^{\prime \prime} \) by implicit differentiation. \[ \begin{array}{c} \cos (y)+\sin (x)=1 \\ y^{\prime}=\frac{\cos (x)}{\sin (y)} \\ y^{\prime \prime}=\frac{\sin ^{2}(y) \2 answers -
Solve the initial value problem. (theta) dy/d(theta) + y = sin(theta), (theta)>0 , y(pi/2) = 1. What is y =?
Solve the initial value problem. \[ \theta \frac{d y}{d \theta}+y=\sin \theta, \theta>0, y\left(\frac{\pi}{2}\right)=1 \] \[ y= \]2 answers -
Thank you!
Which function is a solution to the differential equation \( \frac{d y}{d x}=y \sin x ? \) A. \( y=\sin x \cos x \) B. \( y=\frac{1}{2} \sin ^{2} x \) C. \( y=-\frac{1}{2} \cos ^{2} x \) D. \( y=e^{-\2 answers -
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\( \begin{array}{l}\sin (3 x)+\sin (7 x) \\ \cos (7 x)+\cos (-7 x) \\ \sin (3 x)-\sin (-3 x)\end{array} \)2 answers -
Differentiate. \( y=\left(5-x^{2}\right)^{3} \) 4. \( R(x)=\frac{3 x^{2}-x}{\left(x^{2}-1\right)^{2}} \) 2. \( y=\sqrt{9-4 x^{2}} \) 5. \( y=x^{3} \sqrt{3-x} \) \( h(x)=\frac{2 e^{x^{2}}}{(3 x-4)^{3}}2 answers -
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Let \( y \) be the solution of IVP \( y^{\prime \prime \prime}+3 y^{\prime \prime}+3 y^{\prime}+y=0, y(0)=1, y^{\prime}(0)=0, y^{\prime \prime}(0)=1 \). Then \( y(-1)= \) a. \( -e \) b.e c. \( 2 e \)2 answers -
Part a) Given \( y=\sin \left(x^{2}\right) \), find \( y^{\prime} \). Part b) Given \( y=\left(x^{2}+3 x+4\right)^{3} \), find \( y^{\prime} \). Question 3 Given \( y=\sin ^{3}\left(x^{2}\right) \), f2 answers -
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