lim(x→0)(cosx-cos^2x)/x^2

问题描述:

lim(x→0)(cosx-cos^2x)/x^2

cosx(1-cosx)=cosx ×2sin²(x/2)
(cosx-cos²x)/x²= cosx ×2sin²(x/2)/x²
lim(x→0)cosx ×2sin²(x/2)/x²
= lim(x→0)cosx ×sin²(x/2)/2(x/2)²
∵ lim(x→0) sin(x/2)/(x/2)=1
lim(x→0)cosx =1
上面的式子=1/2