how do we prove uniform continuity for some function

Question

How do we prove if the following function

$f(x)=\frac{1}{x}$ $;x>0$

is uniformly continous in $x>\frac{1}{2}$ and not uniformly continous everywhere

and

$f(x)=x^{n}$ is uniformly continous in [$\frac{1}{2},\frac{3}{4}$] and not in [0,1].