Limit statement; True or False

**VectorRun** · October 14th 2010, 08:33 PM

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.

**Gusbob** · October 14th 2010, 08:46 PM

Consider

$\displaystyle \lim_{x\rightarrow \infty} \sin x$ in the domain $[0,\infty]$

**VectorRun** · October 14th 2010, 09:32 PM

Ah, right...I can't believe I forgot about trigonometric functions. Gosh, how silly of me. Thanks for the help.

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