lim (x->2) (ax^2 - b)/(x-2) = 4 ; Find a and b .?

lim (x->2) (ax^2 - b)/(x-2) = 4 ; Find the solution of a and b .

4 Answers

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  • s k
    Lv 7
    9 years ago
    Favorite Answer

    As x -> 2, x - 2 -> 0. So for the limit to exist, ax^2 - b -> 0 as well.

    By l'Hopital, then,

    lim_{x->2} (ax^2 - b)/(x - 2)

    = lim_{x->2} 2ax = 4.

    So a = 1.

    lim_{x->2} x^2 - b = 0.

    So b = 4.

  • 9 years ago

    A possible answer is a = 2, and b = 4.

  • Ovidiu
    Lv 6
    9 years ago

    (ax^2-b)/(x-2)=

    (x+2)(x-2)/(x-2)=x+2=4

    ax^-b=x^2-4

    a=1

    b=4

  • 9 years ago

    sub x=u+2 and lim = lim u->0 [[a(u+2)^2-b]/u]

    =lim u->0[au+4a +(4a-b)/u] and to equal 4 requires 4a=4 and 4a-b=0

    and you can now complete.

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