求x→0时lim(x-arcsinx)/(sin^3)x的极限

令t=arc sinx 则 x =sint x→0时t→0
所以
原式=(等价无穷小代换)lim (x -arcsinx)/x³
=lim (sint -t)/sin³t
=lim (sint - t)/t³
=（洛毕达）lim (cosx-1)/3t²
=（连续用洛毕达）
=-1/6