1. f(x,y,z) = e^(x^2+y^2)

Eval the gradientWhat is the value of the gradient in the origin? Ifdel Fand is it perpendicular to the isovalue surfaces?

ris any 3D vector and s a real parameter, evaluatedf(sr)

ds

2.F(x,y) = -cosx ei -2y ej

Determine the curldel x F. Is the force conservative. If so find the scalar potential V (x,y) from whichFarises.

By evaluating a line integral, compute the total workW done against the force field F when the particle moves from the point A = (-Pi/2,-1) to the point B = (Pi/2,1) along the segment (a Pi/2, a) for -1 <a < 1. Does the work W depend on the path taken to go from A to B? Give an expression forW in terms of the potential V , without evaluating any integral.