lim(x->0) (arctanx - sinx )/x^3 (0/0 分子分母分别求导)
=lim(x->0) ( 1/(1+x^2) - cosx )/(3x^2)
=lim(x->0) [ 1-(1+x^2)cosx ]/[ (3x^2).(1+x^2) ]
=lim(x->0) [ 1-(1+x^2)cosx ]/ (3x^2) (0/0 分子分母分别求导)
=lim(x->0) [ (1+x^2)sinx -2x.cosx ]/ (6x)
=(1/6) lim(x->0) [ (1+x^2)(sinx/x) -2cosx ]
= (1/6) ( 1- 2)
=-1/6
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