lim(cosx-1)/x,x趋于0,怎么化简成-sinx?

分类: 作业答案 • 2022-04-12 00:00:36

问题描述：

答

cosx-1=1-2sin²(x/2)-1=-2sin²(x/2)
lim(cosx-1)/x=lim[-2sin²(x/2)]/(x/2) *(1/2)=lim[-sin(x/2)]=0

答

lim【x→0】(cosx-1)/x
=lim【x→0】(-x²/2)/x
=lim【x→0】-x/2
=0