Question

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

Answer 1

`lim_(x->0)(sin(x)/(3x)) = 1/3.`

See explanation below.

Explanation:

`lim_(x->0)(sin(x)/(3x)) = "0/0"` so we can use Bernouilli L'Hôpital's rule.

`lim_(x->0)(sin(x)/(3x)) = lim_(x->0)((sin(x)')/((3x)')) =lim_(x->0) cos(x)/3 = 1/3.`