(Section 17.3, 17.5) Consider F(a, y) = (e-" cos(y))i + (e-" sin(y))} (a) Show that F is conservative. (b) Find the potential function f(x,y) for the field F. (c) Evaluate F. dr = F Tds, where C is the line segment from (-1,1) to (1, 1).

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A: fx,y,z=z2x+y3 P1,1,2v→=15i+25j We know directional derivative Dv→fP=∇fP.v→v→

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A: The domain is the set of all values of x for which the value of function f(x) exists.   For f(x)=4-x…

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A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

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A: Given :   f ( x, y) = exy x4   point ( 3,5)

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A: We have to prove

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A: The given function isf(x, y)=sinxy

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A: Given rt=<t sin t+cos t,2t2,sin t -t cos y> Then vector is given by r→t=t sin t+cos…

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A: The given functions are  f(x) = cos-1x/5 , g(x) = tan-110x   If, h(x) = f(x)/g(x)  Find h'(x) and…

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A: Solve for the equation for the derivative

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Q: Show that fi (x) = cos x , f2(x) = cos 2x are orthogonal on [-7,71]. %3D

A: This is a application of integration problem

Q: Let F = (t + 4) i +² sin(41) j+ t^k, G = e' i+ 4f* cos(t) j+ e$t* k and 512 -i+ 4² j+te²ª k 1 +t H =…

A: Given :  F=(t+4)i+t^ 2 sin(4t)j+t^ 4 k G=e^ t i+4t^ 4 cos(t)j+e^ 5t^ 2  H = (t ^ 5)/(1 + t) * i + 4t…

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A: The function is: f(x)=x3+bx+a, x≤-1bx2-a,      x>-1 So, the function is continuous at x=-1 if…