Find the linearization L(x,y) of the function f(x,y) = e 4* cos (y) at the points (0,0) and 0, The linearization at (0,0) is L(x,y) = (Type an exact answer, using t as needed.) 0. is L(x.y)=D The linearization at 0, (Type an exact answer, using n as needed.)

Q: dy (b) Find ,where y = cos ecx –4 r +7 dx

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A: Suppose f(x,y) be a differentiable function at (a,b). Then linearization of f(x,y) at (a,b) is given…

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Q: Evaluate r(2) and r(-1) for r(t) = (sin 1,12, (1² + 1)~1). %3D

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Q: Write the function f(x,y) = xcosh(x)cos(y) - ysinh(x)sin(y) + i(xsinh(x)sin(y) + ycosh(x)sin(y)) in…

A: f(z)=Re(z)cosh(Re(z))cos(Im(z))−Im(z)sinh(Re(z))sin(Im(z))+i(Re(z)sinh(Re(z))sin(Im(z))+Im(z)cosh(Re…

Q: 49y" — 42y + 5y = 0, and - y(4) = 4, y'(4) = 1. y =

A: 49y''-42y'+5y=0, y(4)=4, y'(4)=1 Auxiliary equation 49m2-42m+5=0

Q: a) Find the derivative of f(x,y) = xe* +cos(xy) at the point (2,0) in the direction of V = 3i – 4 j.

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Q: lf f(z, y) = 5ery + 1 sín (inr + y) + 2r + 3y, find-a-,-,-and

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A: Given:rt=sint , t2, t2+1-1

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Q: Find the differential dy of the function y = 4x²-x+ 3 Select one: O a. (8x-1)dx O b. (x²-x² + 3x) dx…

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Q: te r'"(t) and r'(t) for the fo

A: Given that : The function is r(t) =t+4 i + tt +7 j - e-t2 k .

Q: Are the functions f, g, and h given below linearly independent? f(x) = et – cos(5æ), g(x) = e* +…

A: The functions are linearly dependent :

Q: Find fyæy for the function f(x, y) = x² cos(y) +3\/y+ Vy + + Vy? + 3.

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Q: Either f,g,h € F(R, R) the functions f(x) = sin(x)^2 And g(x) = cos(x) and h(x) = sin(x). Show that…

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Q: 3. Find the derivative of the function f(x, y, z) = xy + yz + zx at the point (1,-1, 2) in the…

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Q: Determine whether the functions fi(x) = cos 3r, f2(x) = x, and f3(x) = cos² r independent on the…

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Q: Determine whether the functions y₁ and y₂ are linearly dependent on the interval (0,1). y₁ = tan…

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