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

Question

7762 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-02T21:10:38

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

See explanation below.

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

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

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