limits

lim (x → 0) x2/(cos 2x - 1)

= lim (x → 0) x2/(-2 sin2 x)

= - (1/2) lim (x → 0) x2/(sin2 x)

= -1/2 since lim (x → 0) x/(sin x) = 1

2010-09-27 22:59:29 補充：
Using:

cos 2x = cos^2 x - sin^2 x, we have:
cos 2x - 1 = cos^2 x - sin^2 x - 1 = -2cos^2 x

So for limit of x^2/(-2 sin^2 x), we can extract out -1/2, then

lim x^2/(sin^2 x) = (lim x/sin x)^2 = 1^2 = 1