1. (10pts) Let fn(x) = x3/(1 + 23)" and consider f (x) = >fn(x). n=0 (a) Use a geometric series to show that f(x) = 1 + x3 for x * 0. (b) Does the series converge uniformly on R? Does the series converge uniformly on [-1, 1]. Justify your answer. 2. (10pts) Let fn : [2, 3] - R be defined by fn(a) = (1+x) . (a) Use ratio test to prove that _- In(x) is convergent for x E 2, 3] (b) Is it uniformly convergent