Limit question

**anderson** · February 15th 2010, 11:39 PM

hi everyone

how do i prove $ \lim_{x\rightarrow\infty}\frac{\ln x}{x}=0 $

using L Hospital's rule?

need some help on this question, really appreciate all your help & guidance.

**Prove It** · February 15th 2010, 11:46 PM

Originally Posted by anderson

hi everyone

how do i prove $ \lim_{x\rightarrow\infty}\frac{\ln x}{x}=0 $

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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