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Math Help - Limits

  1. #1
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    Limits

    Evaluate this limit:

    lim as x goes to pi from the left ln(cosx/x)

    I got the answer as pi


    is this right?

    My steps:

    ln(cospi/pi)

    ln(-1/pi)

    ln(-1)=pi

    Am I right or in the right direction?

    Thanks!
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  2. #2
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    Re: Limits

    Quote Originally Posted by Steelers72 View Post
    Evaluate this limit:
    lim as x goes to pi from the left ln(cosx/x)
    The logarithm of negative numbers are not defined.
    So can the limit exist?
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  3. #3
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    Re: Limits

    so it would be DNE?

    I double checked on my calculator and it says ln(-1) would be pi..

    Is there an instance, or another way of asking the problem that would make pi the answer? Im just trying to find other ways the teacher could ask this for an exam.

    Thanks
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  4. #4
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    Re: Limits

    Quote Originally Posted by Steelers72 View Post
    I double checked on my calculator and it says ln(-1) would be pi..

    Is there an instance, or another way of asking the problem that would make pi the answer? Im just trying to find other ways the teacher could ask this for an exam.
    Are you in a complex analysis course?

    If so, then \log(-1)=\pi i.

    But for courses is real analysis, that is not defined.
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  5. #5
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    Re: Limits

    Quote Originally Posted by Steelers72 View Post
    ln(-1/pi)

    ln(-1)=pi
    Your question has been answered by Plato but I want to draw your attention to the last two lines of your calculation.

    You cannot take \pi out of a logarithm. In short:
    ln \left ( \frac{-1}{\pi} \right ) does not imply ln(-1) = \pi.

    ( ln(-1/pi) doesn't exist anyway, but it's the operation I'm objecting to.)

    -Dan
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