Let the metric space $X=(0,\infty)$ and determine whether the following are uniformly continuous on $X$:
(1) $f(x)=\sqrt{x}$
(2) $f(x)=1/x$
(3) $f(x)=\ln(x)$
(4) $f(x)=x\ln(x)$
Since this isn't $\mathbb{R}$ I don't think I can use the usual method: showing that |f'| is bounded.
Any tips on how to solve these problems?