(a) Let f(x) = e, x>0. Use induction to prove that, for every n > 1, the n'th derivative f(n) (x) is of the form Pn(1/x) efor some polynomial Pn (depending on n). (b) Define g(x) = {o 0 if x < 0 e if x>0. Use part (a) and the limit definition of derivative to prove that g(n) (0) = 0 for all n > 1. c) Conclude that function g of part (b) is not equal to the sum of its Maclaurin series.