Which of the following series and integrals converge uniformly?

[Like Tony Stark]

Tell me if I'm wrong, please
The first one doesn't converges uniformly since x^n diverges on [0;2]
The second one converges uniformly: we can apply the M test using the same function without x
And what about the third one?

 

[Like Tony Stark]

The first one doesn't converges uniformly since x^n diverges on [0;2]

I've done my calculations again and found out that it converges