# How do you find the limit of (sin(x)/3x)  as x approaches 0 using l'hospital's rule?

Mar 2, 2016

${\lim}_{x \to 0} \left(\sin \frac{x}{3 x}\right) = \frac{1}{3.}$
${\lim}_{x \to 0} \left(\sin \frac{x}{3 x}\right) = \text{0/0}$ so we can use Bernouilli L'Hôpital's rule.
${\lim}_{x \to 0} \left(\sin \frac{x}{3 x}\right) = {\lim}_{x \to 0} \left(\frac{\sin \left(x\right) '}{\left(3 x\right) '}\right) = {\lim}_{x \to 0} \cos \frac{x}{3} = \frac{1}{3.}$