(a) For every x ＞ O, determine Let f(x) be the function given by the pointwise limit you found in part (a).

(4) [20 分] Let F be a smooth map from R3 to R3. Denote by (x1, x2, x3) the coordinate for the domain R3. Denote the origin (0,0,0) by 0. Suppose that Prove that there exist ●open neighborhoodsof O in (the domain) R3, and a diffeomorphism φ :which maps O to O, ●open neighborhoodsof O in (the target) R3, and a diffeomorphism V which maps O to O, What follows is the diagram for your reference.