原式=limx→0 [tanx-tan(sinx)]/x^3*limx→0 sinx/x*limx→0 x/arctanx
=limx→0 [1/cos^2x-cosx/cos^2(sinx)]/3x^2*1*1
=limx→0 [cos^2(sinx)-cos^3x]/3x^2*limx→0 1/[cos^2x*cos^2(sinx)]
=limx→0 [-2cos(sinx)sin(sinx)cosx+3cos^2xsinx]/6x*1
=limx→0 [3sin2x-2sin(2sinx)]/12x*limx→0 cosx
=limx→0 [6cos2x-4cos(2sinx)*cosx]/12
=(6-4)/12
=1/6.
内容全部来源于网络收集，如有侵权，请联系网站删除：QQ：24596024