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Thread: Limit Tan and cos

  1. #1
    Super Member dhiab's Avatar
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    Limit Tan and cos

    Calculate :
     <br />
\lim_{x\to +\infty }(x^{2}+xtan(x))<br />
    \lim_{x\to +\infty }(\sqrt{\cos (2\Pi x)-1})
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  2. #2
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    Quote Originally Posted by dhiab View Post
    Calculate :
     <br />
\lim_{x\to +\infty }(x^{2}+xtan(x))<br />
    \lim_{x\to +\infty }(\sqrt{\cos (2\Pi x)-1})
    It's pretty obvious, isn't it, that the first will go to infinity (there is no limit).

    And the second also does not have a limit because it oscillates.
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  3. #3
    MHF Contributor ebaines's Avatar
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    Quote Originally Posted by HallsofIvy View Post
    It's pretty obvious, isn't it, that the first will go to infinity (there is no limit).

    And the second also does not have a limit because it oscillates.
    I disagree. The first one oscillates between positive and negative infinity, and hence has no limit.
    The second one is undefined for all but integer values of x, in which case it evaluates to 0. So it's limit is undefined.
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