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Calculus problem on finding limits?

How do you find the limit as x -> -1 for the equation ((x^2 + 8)^(1/2) - 3) / (x + 1)

Update:

Can someone explain without using derivatives?

2 Answers

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  • Anonymous
    8 years ago
    Favorite Answer

    Use L'Hopital's rule. Take the derivative of the numerator and the denominator:

    d/dx (x^2 + 8)^(1/2) - 3 = (1/2)*(x^2+8)^(-1/2)*2x

    d/dx x + 1 = 1

    So plug in x = -1:

    (1/2)*((-1)^2+8)^(-1/2)*2*(-1)

    =(1/2)*(9)^(-1/2)*-2

    =-1*(1/3) = -1/3

    The limit is -1/3

  • plug in x = -1 + h to the equation

    why? because that's the limit of tangent line, lim as h->0 f(a+h)-f(a) / h

    something like that (I forget, its been awhile)

    so your equation should be lim h->0 ( your original equation with x = -1 +h)

    and your answer should be -1/3

    just like the person above.

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