Plz refer to the pic for the question

2. Consider the function f : R2 - R3, f (u, v) = (2 . cos u, 2 . sin u, v) (a) For each v E R fixed, describe the transformation effect of f on the set Rx {v} ; illustrate using a schematic sketch. (b) For each u E R fixed, describe the transformation effect of f on the set {u} x R; illustrate using a schematic sketch. (c) Show that f transforms R2 into the surface given by a2 + y? = 4. (d) For each a = (a, b) E R2 find the total derivative of f at a. With el = (1,0) and e2 = (0, 1) , compute the vectors Daf (e1) and Daf (e2) (e) For a as in part (d), let 61, 62: R - R2 be the functions given by li(t) = a + tel and 12 (t) = a + te2 Compute foll and f ol2 and identify their traces. Compare (f ol1)'(0) and (f o (2)'(0) with the vectors computed in the part (d). - Explain