用泰勒公式算极限lim (sinx-xcosx)/(sinx的三次方)

Question

如题所述

Answer 1

x->0
cosx ~ 1- (1/2)x^2
sinx ~ x - (1/6)x^3
sinx - xcosx ~ (1/3)x^3
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lim(x->0) (sinx-xcosx)/(sinx)^3
=lim(x->0) (1/3)x^3/x^3
=1/3本回答被网友采纳

Answer 2

分母无穷近似值代换为x³后再泰勒级数展开