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Math Help - Stuck on a STEP function about continuity.

  1. #1
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    Question Stuck on a STEP function about continuity.

    Find the largest value of k for which the function defined by

    is continuous on the interval [3, 3+k) .

    ...Through aproximation I found that in order to stay in one "step" the interval has to be [3, <sqrt(10)) but I can't seem to find a way to find k algebraically from the beginning.
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  2. #2
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    Quote Originally Posted by Arturo_026 View Post
    Find the largest value of k for which the function defined by

    is continuous on the interval [3, 3+k) .

    ...Through aproximation I found that in order to stay in one "step" the interval has to be [3, <sqrt(10)) but I can't seem to find a way to find k algebraically from the beginning.
    Well
    Because \left\lfloor {3^2  - 2} \right\rfloor  = 7
    we know that x^2-2<8
    so x^2<10.
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  3. #3
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    Quote Originally Posted by Plato View Post
    Well
    Because \left\lfloor {3^2 - 2} \right\rfloor = 7
    we know that x^2-2<8
    so x^2<10.
    Right, then i get k < sqrt(10) - 3
    Then, what would be the largest value k can attain?
    Last edited by Arturo_026; September 20th 2009 at 07:20 PM.
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