Evaluate the change in z (i.e., ?z) in going from the point (0,0) to the point (1,1) for the differentials:
(1) dz = (x^2 + y^2) dx + xy dy and (2) dz = xy dx + xy dy
(a) Go from (0,0) to (0,1) keeping x constant and equal to 0; then to (1,1) keeping y constant and equal to 1
(b) Go along the path y=x
(c) Go along the path y = x2.