calculus

1.) Lim [√(x + 1) - (2)] / (x - 3)
x -> 3

2.) Lim [ (1/ x + 4) - (1 / 4)] / (x)
x -> 0

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  1. Take the ratio of the derivatives of numerator and denominator, and evaluate it at the x value in question.

    For both problems, the derivative of the denominator is just 1, so you just have to evaluate the derivative of the numerator.

    In the first problem,
    Lim [�ã(x + 1)-(2)]/(x-3)
    x -> 3

    = (1/2�ã(x + 1)
    = 1/4 at x =3

    For the second problem
    Lim [(1/(x+4)-(1/4)]/ x
    x -> 0
    = -1(x+4)^2 at x=0
    = -1/16

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