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Math Help - Continuous Functions

  1. #1
    Senior Member
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    Continuous Functions

    I'm having some trouble with this question:

    Consider\ the\ function

    f(x)=\frac{x^3-6x^2+11x-6}{x-a}

    This\ is\ not\ continuous\ at\ x=a. For\ which\ values\ of\ a\ is\ the\ disconuity\ removable?
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  2. #2
    MHF Contributor
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    Hi

    The discontinuity is removable if a is a solution of x^3 - 6x^2 + 11x - 6 = 0 because in this case you can write

    x^3 - 6x^2 + 11x - 6 = (x-a) P(x) where P is a second degree polynomial

    And then f(x) = \frac{x^3 - 6x^2 + 11x - 6}{x-a} = \frac{(x-a) P(x)}{x-a} = P(x) is continuous at a
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  3. #3
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by acevipa View Post
    I'm having some trouble with this question:

    Consider\ the\ function

    f(x)=\frac{x^3-6x^2+11x-6}{x-a}

    This\ is\ not\ continuous\ at\ x=a. For\ which\ values\ of\ a\ is\ the\ disconuity\ removable?
    first is x^3-6x^2+11x-6 composite it is

    x^3-6x^2+11x-6 = (x-2)(x^2-4x+3)

    is x^2-4x+3) composite

    so the first value of a is 2

    you can continue
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