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Math Help - Limit question

  1. #1
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    Limit question

    hi everyone

    how do i prove <br /> <br />
\lim_{x\rightarrow\infty}\frac{\ln x}{x}=0<br />

    using L Hospital's rule?

    need some help on this question, really appreciate all your help & guidance.
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  2. #2
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    Quote Originally Posted by anderson View Post
    hi everyone

    how do i prove <br /> <br />
\lim_{x\rightarrow\infty}\frac{\ln x}{x}=0<br />

    using L Hospital's rule?

    need some help on this question, really appreciate all your help & guidance.
    Since this will tend to \frac{\infty}{\infty}, you can use L'Hospital's Rule.

    So \lim_{x \to \infty}\frac{\ln{x}}{x} = \lim_{x \to \infty}\frac{\frac{d}{dx}(\ln{x})}{\frac{d}{dx}(x)  }

     = \lim_{x \to \infty}\frac{\frac{1}{x}}{1}

     = \lim_{x \to \infty}\frac{1}{x}

     = 0.
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