lim(x趋向0)(arctanx-x)/sinx^3

问题描述:

lim(x趋向0)(arctanx-x)/sinx^3

lim【x→0】(arctanx-x)/sinx³
=lim【x→0】[1/(1+x²)-1]/(3x²cosx³)
=lim【x→0】(-1)/[(1+x²)(3cosx²)]
=-1/3
答案:-1/3