Every is continuous on , however:

is not continuous on , so by a well known theorem, the convergence is not uniform.

Yes, nowThen if we were to fix r>0, is it uniformly convergent at [r, infinity]?

Prove that for every there exists such that

for and for all

Possibly is:Also, there was another part of the problem. the professor wrote something like

He's a messy writer, and i do believe that was what he wrote, but Im not too sure if that fits into the problem at all, or if it even does.

Fernando Revilla