(3) (16 points) Consider z= uv, uw=@rot+y, very. (a) (4 points) Express z in the form z = fog where g: R? R? and f: R? (b) (4 points) Use the chain rule to calculate Vz = (2,, 2,) . Show all intermediate steps otherwise no credit. (c) (4 points) Let S be the surface parametrized by T(z,y) =(z.y,f(g(z,y)) (x,y) ER'. Give a parametric description of the tangent plane to S at the point p= T(z, y). (d) (4 points) Calculate the second Taylor polynomial Q(x,y) (i.e. the quadratic approximation) of F = (fog) ata point (a,b). Verify that Q(z,y) = Flat+2,64+y)