Setting the integral becomes...
(1)
Now the function...
(2)
... is monotonically decreasing for nd ...
(3)
... so that is...
(4)
... and the integral converges...
Kind regards
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
Setting the integral becomes...
(1)
Now the function...
(2)
... is monotonically decreasing for nd ...
(3)
... so that is...
(4)
... and the integral converges...
Kind regards