# How do you use L'hospital's rule to find the limit lim_(x->oo)ln(x)/sqrt(x) ?

##### 1 Answer
Sep 6, 2014

By l'Hopital's Rule,
${\lim}_{x \to \infty} \frac{\ln x}{\sqrt{x}} = 0$.

Let us look at this limit in more details.
By l'Hopital's Rule,
lim_{x to infty}{lnx}/sqrt{x} =lim_{x to infty}{1/x}/{1/{2sqrt{x}}}
by multiplying the numerator and the denominator by $2 \sqrt{x}$,
$= {\lim}_{x \to \infty} \frac{2 \sqrt{x}}{x} = {\lim}_{x \to \infty} \frac{2}{\sqrt{x}} = 0$