求极限lim2/πarctanx求极限,当x趋向于无穷时lim（2/π*arctanx）^2x,答案是e^-4/π,

Question

求极限lim2/πarctanx
求极限,当x趋向于无穷时lim（2/π*arctanx）^2x,答案是e^-4/π,

Answer 1

2/π*arctanx）^2x
=(1+2/π*arctanx-1）^2x
=(1+2/π*arctanx-1）^2x*(2/π*arctanx-1)/(2/π*arctanx-1)
=e^2x*(2/π*arctanx-1)
=e^2(2/π*arctanx-1)/(1/x)
罗笔塔法则
=e^-4/π