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Calculus

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is there a number a such that the lim x->2 6x^2+ax+a+57/x^+x-6 exists? if so find the value of a and the limit.

  • Calculus - ,

    You have a fraction with denominator=0 at x=2

    So, you want the numerator to also be zero, or you have no hope of having a limit.

    6x^2 + ax + a + 57 = 0
    24 + 2a + a + 57 = 0
    81 + 3a = 0
    a = -27

    so,

    6x^2 - 27x + 30 / x^2 + x - 6
    =(6x-15)(x-2) / (x+3)(x-2)

    So, the limit = (6x-15)/(x+3) = -3/5

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