A conservative vector field is given by: F= (e^-t (x+y), g(x, y, t)) (a) Find the function g(x, y, t) (b) Calculate the work done if a particle starts at (0,r) and travels in a complete circle around the origin. (c) Find the divergence of the field, and explain in simple words what your answer means. (d) Show that the curl of the vector field is zero (e) Given your answer to parts c and d, explain wether the field conforms to the laplacian identify.