(a) Set up, but do not evaluate, a double integral for the area of the surface with parametric equations x = au cos v, y = bu sin v, z = u², 0 < u < 2, 0 < v < 2.
(b) Eliminate the parameters to show that the surface is an elliptic paraboloid and set up another double integral for the surface area.
(c) Use the parametric equations in part (a) with a = 2 and b = 3 to graph the surface.
(d) For the case a = 2, b = 3, use a computer algebra system to find the surface area correct to four decimal places.