hi everyone
how do i prove$\displaystyle
\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 $\displaystyle \frac{\infty}{\infty}$, you can use L'Hospital's Rule.
So $\displaystyle \lim_{x \to \infty}\frac{\ln{x}}{x} = \lim_{x \to \infty}\frac{\frac{d}{dx}(\ln{x})}{\frac{d}{dx}(x) }$
$\displaystyle = \lim_{x \to \infty}\frac{\frac{1}{x}}{1}$
$\displaystyle = \lim_{x \to \infty}\frac{1}{x}$
$\displaystyle = 0$.