问题标题：
lim/x→3.14/2^+ln(x-3.14/2)/tanx
更新时间：2024-04-28 00:18:30
问题描述：
lim/x→3.14/2^+ln(x-3.14/2)/tanx
戈戟回答：
lim(x->π/2+)[ln(x-π/2)/tanx]=lim(x->π/2+){[1/(x-π/2)]/sec²x}(∞/∞型极限,应用罗比达法则)
=lim(x->π/2+)[cos²x/(x-π/2)](0/0型极限,应用罗比达法则)
=lim(x->π/2+)(-2sinx*cosx)
=lim(x->π/2+)[-sin(2x)]
=-sinπ
=0.
