F(t, x, y, 2) = [0, cos(t), sin(t)] x 7, 0

Q: Determine f g a) f(t) = cos(t), g(t) = t b) f(t)=e¹, g(t) = e' sin(t)

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Q: DEFINITION 10.1.1 Let f be a function defined on an interval [0, o0). The Laplace transform of f is…

A: Lapalce transfermation.

Q: fyx if f(x, y) = sin(xy) + x² In y cos(xy)- xysin(xy) - cos(xy) + xysin(xy) + cos(xy) – xysin(xy) +…

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Q: Use Green's Thoerem to evaluate F dr. where F(r, y) = (-3Vx² + 2, 7 tan '(x)) and C is the triangle…

A: We have to evaluate by Green's theorem.

Q: Find the local extrema of the function f(x, y) = e-(cos(r)+sin(y)) and test for which are max, min,…

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Q: f(r,t) = cos(3r) exp(4t) %3D fi(x,t)+ frz(x,t) = f(r,t) %3D

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Q: Let f(x, y) = x sin ry. Find: fyy (x, y) fyz(x, y)

A: f(x,y)=xsinxyfx=sinxy+xycosxyfyx=xcosxy+x(cosxy-xysinxy)=2xcosxy-x2ysinxyfy=x2cosxyfyy=-x3sinxy

Q: Express the following function in the form f(z)=u(x,y)+iv(x,y) 1. cos(z^2)

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Q: Let f (t) = et sin 8t Part (a) Find L{f(t)}

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Q: (a) Differentiate f(x) = Vx+4 by using the first principle. (b) Differentiate the following…

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Q: Find the extrema of f(x,y)=(x+1)(y+1)(x+y+1)

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Q: Find fxxx for f(x, y) = Sin() at (π, π)

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Q: What is the range of f(r) = cos(x)? i) [–1, 1] ii) [0, 1] iii) (-∞, ∞) O i O i

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Q: Find the linear approximation of the function at the given point: f(x, y) = 2 sin x – 3 cos y at (0,…

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Q: 1-x The equation of the tangent line for y = at (- 2, – 3) is 1+X

A: AS PER GUIDELINES I CAN ATTEMPT ONLY FIRST QUESTION

Q: af If f(x,y) = sin-(4x³y?) then dx 12x?y? 1-(4x³y²)² O a. b. 1 4x³y²/(4x³y?)² – 1 c. 12x²y² 4x³y?…

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

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Q: Calculate c{fie*sin (t - v) du}

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Q: f(x, y) =- sin xcos y, then

A: The given function is: f(x,y)=-sin xcos y To find ∂2f∂x2. Here, note that y is constant w.r.t. x.