limx→0(1⼀sin^3x-1⼀x^3)怎么做

limx→0(1/sin^3x-1/x^3)
=limx→0[(x^3-sin^3x)/(xsinx)^3]
=limx→0{[x^3-(x-x^3/6)^3]/x^6]}
=limx→0{(x^5/2-x^7/12+x^9/216)/x^6]}
=limx→0{(1-x^2/12+x^4/216)/x]}→无穷，极限不存在，
是否看错了题目？把平方看成了立方，把立方改成平方：
lim(x→0)(1/sin^2x-1/x^2)
=lim(x→0)[(x^2-sin^2x)/(xsinx)^2]
=lim(x→0){[x^2-(x-x^3/6)^2]/x^4]}
=lim(x→0){(x^4/3-x^6/36)/x^4]}
=lim(x→0)(1/3-x^2/36)=1/3

lim[1/(sinx)^3 - 1/x^3] = lim[x^3-(sinx)^3]/(xsinx)^3
= lim[x^3-(sinx)^3]/x^6 (0/0)
= lim[x^2-(sinx)^2cosx]/(2x^5) (0/0)
= lim[2x-2sinx(cosx)^2+(sinx)^3]/(10x^4) (0/0)
= lim[2-2(cosx)^3+7cosx(sinx)^2]/(40x^3) (0/0)
= lim[20sinx(cosx)^2-7(sinx)^3]/(120x^2)
= lim[20(cosx)^2-7(sinx)^2]/(120x) = ∞