# Limit statement; True or False

• Oct 14th 2010, 09:33 PM
VectorRun
Limit statement; True or False
If f has domain [0, $\infty$) and has no horizontal asymptotes, then $\lim_{x\to\infty}{f(x)=\infty$ or $\lim_{x\to\infty}{f(x)=-\infty$.

The answer is false...But I'm having a difficult time ascertaining why that is the case. I might be interpreting the statement wrong...I don't know. Could I get some advice? Thanks a lot.
• Oct 14th 2010, 09:46 PM
Gusbob
Consider

$\displaystyle \lim_{x\rightarrow \infty} \sin x$ in the domain $[0,\infty]$
• Oct 14th 2010, 10:32 PM
VectorRun
Ah, right...I can't believe I forgot about trigonometric functions. Gosh, how silly of me. Thanks for the help.