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Math Help - One sided limits.

  1. #1
    Junior Member Kaloda's Avatar
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    One sided limits.

    Find: \lim_{x\to 0-}\sqrt{x^3-x}.

    Our teacher said that the limit exists for this function namely, 0, but our book tells that the limit doesn't exist.
    He argued that the limit exists because the domain of the function is [-1,0]\cup[1,\infty)
    which includes negative nos. from -1 to zero (less than -1 will make the function imaginary).

    Which is correct?
    Last edited by Kaloda; July 19th 2012 at 05:01 AM.
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  2. #2
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    Re: One sided limits.

    Teacher is correct because if you take 0-h as h->0, the function is well defined in the neighborhood and also defined at x=0. So LHL does exist.
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  3. #3
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    Re: One sided limits.

    Quote Originally Posted by Kaloda View Post
    Find: \lim_{x\to 0-}\sqrt{x^3-x}.

    Our teacher said that the limit exists for this function namely, 0, but our book tells that the limit doesn't exist.
    What exactly does your book say about this particular limit? Simply that it does not exist?
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  4. #4
    Junior Member Kaloda's Avatar
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    Re: One sided limits.

    @emakarov:

    Yea, because it's a question in a practice test so the book gives only the answer and not the solution.
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  5. #5
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    Re: One sided limits.

    I agree with pratique and your teacher that the limit exists.
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