Prove:

If $\displaystyle f(x)$ is continius function on $\displaystyle [0,\infty)$ and if $\displaystyle lim_{x\to \infty} f(x)=M<\infty$, then $\displaystyle f(x)$ is bounded on$\displaystyle [0,\infty]$

What I did..

I looked the next two intervals:

1. $\displaystyle [0,M]$, $\displaystyle f(x)$ is bounded there.

2. $\displaystyle [M, \infty)$, and I don't know what to do next here...

Thanks!