x->0,1-cosx~1/2*x^2
lim (x->0) 1-cosx/x^2 = lim(x->0)1/2*x^2/x^2=1/2
这是用等价无穷小的做法,你也可以直接利用洛必达法则来做
lim (x->0) 1-cosx/x^2 = lim(x->0)sinx/2x = 1/2lim(x->0)sinx/x = 1/2*1=1/2
(lim(x->0)sinx/x = 1是重要极限)