Hi, so Im studying for finals and am stuck on a problem. I got referred to this forum from a friend, and I had a quick question about uniform convergence.

we have a function which is:

$\displaystyle f_n(x)\frac{nx}{nx+1}$ for all n greater than or equal to 1.

Is this uniformly convergent at [0,1]?

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

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

$\displaystyle f(x) = \lim_{x\to\infty}f(x^n)$

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.

Any help is appreciated. Thanks!