作业帮limx趋近于0 2cos2xsinx / 2sin4xcosx 为啥cos2x/cosx的极限等于一啊
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/10 19:21:56
limx趋近于0 2cos2xsinx / 2sin4xcosx 为啥cos2x/cosx的极限等于一啊
limx趋近于0 2cos2xsinx / 2sin4xcosx 为啥cos2x/cosx的极限等于一啊
limx趋近于0 2cos2xsinx / 2sin4xcosx 为啥cos2x/cosx的极限等于一啊
x→0时,直接代入就可以得出cos2x/cosx＝1
lim(x→0) cos2x/cosx=lim(x→0)[2(cosx)^2-1]/cosx
=lim(x→0)2cosx-1/cosx
=2-1=1
lim(x→0)(2cos2xsinx)/(2sin4xcosx)
=lim(x→0) (2cos2xsinx)/[2(2sin2xcos2xccosx]
=lim(x→0)sinx/[2(2sinxcosx)cosx]
=lim(x→0)1/(4(cosx)^2)
=1/4
limx趋近于0 2cos2xsinx / 2sin4xcosx 为啥cos2x/cosx的极限等于一啊
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