求极限lim[cos(x+h)-cosx]/hh->0-=

题目详情

求极限
lim [cos(x+h)-cosx]/h
h->0
- =

▼优质解答

答案和解析

因为cos(x+h)-cosx=-2sin(x+h/2)sin(h/2)
所以:lim [cos(x+h)-cosx]/h
=lim[-2sin(x+h/2)sin(h/2)/h]
=lim[-sin(x+h/2)sin(h/2)/(h/2)]
=lim[-sin(x+h/2)]
=-sinx

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