\begin{align*}&\lim_{x\to0^+}\cot x(\frac{1}{\sin x}-\frac{1}{x})\\ =&\lim_{x\to0^+}\frac{x-\sin x}{x\sin x\tan x}\\ =&\lim_{x\to0^+}\frac{\frac{1}{3!}x^3+o(x^3)}{x^3}\cos x\\ =&\frac{1}{6}\end{align*}
posted on 2015-09-10 11:55 Marlinhz 阅读(226) 评论(0) 编辑 收藏 举报