I'll be glad to get some help in the following questions:
1. Let g(x) be a differentiable function at which satisfies: is a monotonic ascending function at
and: , g'(x) is continous at .
Check whether the integral converges.
2. Let f(x) be a function defined by: .
Prove that if the series converges then f(x) is differentiable for every real x.
Thanks in advance