Limits: Finding the Value of (x - Sinx) / x^3

[rambo5330]

Homework Statement

lim (x->0) of (x - Sinx) / x^3

Homework Equations

The Attempt at a Solution

I would like to know the proper route for analyzing that question... the text is saying i should end up with 1/6 ...however I'm not sure how they arrived at that answer ...

 

[flyers]

Are you familiar with l'hopitale's rule?

if lim (x->0) a/b = 0/0 or infinity/infitity then lim (x->0) a/b = lim (x->0) a'/b'

 

[rambo5330]

not familiar with that yet ...

 

[Mark44]

Another approach is to replace sin x by a few terms of its Maclaurin series, but if you don't know L'Hopital's Rule, you probably don't know anything about series yet, either. Short of those two techniques, I can't think of anything else that would work for you.