L I M x → 0 ( tanx-sinx)/x^3
=L I M x → 0 [tanx*(1-cosx)]/x^3
=L I M x → 0 [tanx*(1-cosx)]/x^3
由洛必达法则：
L I M x → 0时 tanx~x
L I M x → 0时1-cosx~1/2*x^2
所以,
L I M x → 0 [x*(1/2*x^2)]/x^3
=L I M x → 0 (1/2*x^3)/x^3
=1/2