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.