lim(x趋向于0）(1+sinx-cosx)/(1+sinβx-cosβx)

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/09/29 20:59:00

(1+sinx-cosx)/(1+sinβx-cosβx)
=（sinx+2(sin(x/2))^2)/（sinbx+2(sin(bx/2))^2)
=[(sin(x/2)+cos(x/2))/(sin(bx/2)+cos(bx/2))]*(sin(x/2)/sin(bx/2))
极限与下式的极限相等
(cos(x/2)/cos(bx/2))*(sin(x/2)/sin(bx/2))
=sinx/sinbx极限为1/b.

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