3.

(b) First prove that if g(x) =

e- l / x2 /xk for some kEN, then g(x) ----> 0 as x ----> O. Next, prove that given n E N, there are integers N = N(n) E Nand ak = akn ) E Z such that xi-O x=O.

(Note: Although for each n E N many of the ak's are zero, this fact is not needed in this exercise.)