极限limx趋近于0 (sin(sinx)-sinx)/x^3怎么求?_数学解答

极限limx趋近于0 (sin(sinx)-sinx)/x^3怎么求?

人气：442 ℃　时间：2020-04-04 22:30:00

解答

原式=limx→0 [cos(sinx)*cosx-cosx]/3x^2,
=limx→0 [cos(sinx)-1]/3x^2
=limx→0 -sin(sinx)*cosx/6x
=limx→0 -sin(sinx)/6x
=limx→0 -cos(sinx)*cosx/6
=-1/6.