求极限 (tanx-x）除以ln（1+x的三次方）.x是趋向于0.……

题目

求极限 (tanx-x）除以ln（1+x的三次方）.x是趋向于0.……

答案

lim(tanx-x)/ln(1+x^3)
=lim(sinx-xcosx)/(x^3cosx)
=lim(sinx-xcosx)/(x^3)
=lim(cosx-cosx+xsinx)/3x^2
=limxsinx/3x^2
=1/3