Given the vector field f = zi + 2yzj + (x + y 2 )k.

(a) find the divergence of the field.
(b) find the curl of the field.
(c) is the given field conservative? if it is, find a potential function.
(d) compute z c z dx + 2yz dy + (x + y 2 ) dz where c is the positively oriented curve y 2 + z 2 = 4, x = 5.
(e) compute z c z dx + 2yz dy + (x + y 2 ) dz where c consists of the three line segments: from (0, 0, 0) to (4, 0, 0), from (4, 0, 0) to (2, 3, 1), and from (2, 3, 1) to (1, 1, 1).