Find the limits of the following functions. of the following functions. Find an interval on which convergence is uniform and another on which it is not.
$f_n(x) = (x/2)^n +(1/x)^n$
For $h_n(x) = (n+x)/(4n+x)$ show it converges uniformly on $[0,N]$ for any $N \lt \infty$ but not uniformly on $[0,\infty)$.
My text only has the theorem regarding uniform continuity so any help as to what algorithm is used for these type of questions would be greatly helpful