Hey there,

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