$f:[0,\infty) \rightarrow \mathbb{R}$ is continuous.
Given $f$ satisfies $\epsilon>0$ there exists $M_{\epsilon} > 0$ such that $x>M_{\epsilon} \implies |f(x)| < \epsilon$
Prove uniform continuity on $[0,\infty)$.
Since $[0,\infty)$ is a subset of $\mathbb{R}$, $f$ is uniformly continuous if for each $\epsilon > 0$ there is a $\delta > 0$ such that $||F(x) - F(y) ||<\epsilon$ when $x,y \in [0,\infty)$ and $||x-y||<\delta$
I also know that a continuous function on a closed bounded interval is uniformly continuous but I'm not sure that this fact helps us. I am stuck on how the given information helps us.