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Thread: L'hospitals rule

  1. December 8th 2008, 12:33 PM #1
    Lone21
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    L'hospitals rule

    so i have this problem and i know that it converges to 0 but i dont know why
    can someone help me

    lim x->(infinity) (lnx)^3/x^2
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  2. December 8th 2008, 02:21 PM #2
    chabmgph
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    Quote Originally Posted by Lone21 View Post
    so i have this problem and i know that it converges to 0 but i dont know why
    can someone help me

    lim x->(infinity) (lnx)^3/x^2
    Hi Lone21,

    Since the numerator and the denominator both go to inf. as x goes to inf.
    We can apply L'Hospital's Rule:
    As {x\rightarrow infinity}, \lim \frac{(\ln x)^3}{x^2}=\lim \frac{3(ln x)^2 * \frac{1}{x}}{2x}= \lim \frac{3(ln x)^2 }{2x^2} =...

    Just keep applying L'Hospital's Rule and simplify your answer in each step.
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