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!