Compute lim as x approaches 0

1. The problem statement, all variables and given/known data

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

2. Relevant equations

Compute the lim

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

Dick

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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.
 
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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.
 

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