(a) Find an equation of the tangent plane at the point (4, -2, 1)to the parametric surface S given by r(u, v) = v² i - uv j + u² k 0 < u < 3, -3 < v < 3

(b) Use a computer to graph the surface S and the tangent plane found in part (a).
(c) Set up, but do not evaluate, an integral for the surface area of S. 

(d) Iffind ∫∫_S F • dS correct to four decimal places.

Transcribed Image Text:

x? .2 z? i+ 1 + x? F(x, y, z) y? -k 1 + z? = I+ y2j + 2.