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Math Help - Limits at x = 0?

  1. #1
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    Limits at x = 0?

    What is the limit of \sqrt(x-x^2) as x\to 0. I know the limit of \sqrt(x-x^2) as x\to 0+ is 0, but since the limit doesn't exist as x\to 0-, is there a limit as x\to 0?
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  2. #2
    Super Member Aryth's Avatar
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    A limit L exists if and only if:

    \lim_{x\to a^+} = \lim_{x\to a^-} = L

    There are more requirements, but this is what pertains to your problem.
    Last edited by Aryth; October 7th 2008 at 09:08 AM.
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  3. #3
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    So that Means No limit exists?
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  4. #4
    Super Member Aryth's Avatar
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    Exactly. You have to be able to arrive at the same limit from both directions. If one does not exist or is not equal to the other, then no limit exists.
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  5. #5
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    TYVM.
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    Senior Member pankaj's Avatar
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    O.K..Can one say that f(x)=\sqrt{x-x^2} is continuous at x=0.
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  7. #7
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    Quote Originally Posted by pankaj View Post
    O.K..Can one say that f(x)=\sqrt{x-x^2} is continuous at x=0.
    Yes. The domain is [0,1] and since \lim_{x\to 0^+} f(x) = f(0) it is continous.
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  8. #8
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    Quote Originally Posted by ThePerfectHacker View Post
    Yes. The domain is [0,1] and since \lim_{x\to 0^+} f(x) = f(0) it is continous.
    So the limit to my question is 0?
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  9. #9
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    Quote Originally Posted by kbartlett View Post
    So the limit to my question is 0?
    Yes
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