Expert: Ahmed Salami - 1/8/2005

Question
I can't find the Limit
lim x->0 (x-tan 2x)/(sin 2x)
Help

Answer
Hi Georgia,
Please forgive the delay. I was on vacation.
Inserting x directly results in 0/0 which is indeterminate. We therefore use L'hopital's rule which asks us to differentiate both top and bottom separately before inserting the limit. Differentiating top and bottom separately gives
1 - 2sec^2(2x) / 2cos 2x
inserting x = 0 then gives 1-2/2
= -1/2
I hope you get it.
Regards.