What is the Limit of a Function as x Approaches 0?

[bumpercars21]

Homework Statement

http://i45.tinypic.com/20rsnis.jpg

Homework Equations

Compute the lim

The Attempt at a Solution

I tried using l'Hopital's rule but I have to keep finding the derivative and it doesn't yield an answer. I have to use taylor series for the trig functions, but don't know how this will work

 

[Dick]

Go ahead, try it. Expand cos(2x) and sin(x) in a taylor series. See which terms cancel. If you don't know the expansion of cos and sin, they are easy to look up.

 

[cap.r]

http://en.wikipedia.org/wiki/Taylor_series

a good rule of thumb is to turn sin and cosine and even e into their taylor series whenever doing limit problems. then subtract whatever you can. and factor out as many x terms as you need to make the top and bottom non zero. and then calculate the limit.