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Math Help - Limit statement; True or False

  1. #1
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    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.
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  2. #2
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    Consider

     \displaystyle \lim_{x\rightarrow \infty} \sin x in the domain  [0,\infty]
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  3. #3
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    Ah, right...I can't believe I forgot about trigonometric functions. Gosh, how silly of me. Thanks for the help.
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