x趋向0 lim(cot x- 1/x)=?

题目

x趋向0 lim(cot x- 1/x)=?

答案

x→0时cotx-1/x
=cosx/sinx-1/x
→(cosx-1)/x
=-2[sin(x/2)]/x
→-2(x/2)^2/x
=-x/2→0.