# Math Help - Limit question

1. ## Limit question

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.

2. 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 $\lim_{x \to \infty}\frac{\ln{x}}{x} = \lim_{x \to \infty}\frac{\frac{d}{dx}(\ln{x})}{\frac{d}{dx}(x) }$

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

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

$= 0$.