lim x→0(tanx-x)/x^2sinx用洛必达法则解答

来源：学生作业帮编辑：百度作业网作业帮分类：数学作业时间：2024/05/13 17:06:10

lim(x->0)(tanx-x)/(x^2sinx）=lim(x->0)(sinx-xcosx)/((1/2)x^2sin2x)
=lim(x->0)(sinx-xcosx)'/((1/2)x^2sin2x)'
=lim(x->0)(cosx-cosx+xsinx)/(xsin2x+x^2cos2x)
=lim(x->0)(xsinx)/(xsin2x+x^2cos2x)
=lim(x->0)(1/(2cosx+(x/sinx)cos2x))
=1/3

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