Consider the vector function F(x,y,z)=<e^xsiny+z/y ,e^xcosyxz/y²,x/y1/z>.

(a) Show that F(x,y,z)is a conservative vector field.

(b) Find a potential function f(x,y,z)

for F(x,y,z) so that you can express F as a gradient vector field: F=f.

(c) Evaluate _cF(x,y,z)drwhere C is a unit circle centered at zero in the xz-plane.

(d) Find the work done if F(x,y,z) N is a force field, and a particle is moved along a line segment C from (1,/2,1) to (0,,e)

in metres.