Hello!

I am working on what seems to be a very "concrete" exercise in showing convergence.

on the interval , show that the functions converge to the function f(x) point-wise, and determine if they converge uniformly.

a) where

b) where

c) where

What I've got so far...

So, to show a function is convergent point-wise, we just try to show that the NUMBER sequence converges to so, such that implies

Here is where I get confused. Do we define an epsilon in terms of n?! Which would depend on the series of functions in all 3 cases?

And for uniform convergence, we are seeking a similar result but with an epsilon which is independent of n?

Any help/guidance to set up the question further appreciated!!