lim x→+∞(π/2-arctanx)/ln(1+1/x)
=lim x→+∞(-1/[1＋x²])/1/(1+1/x)·[-1/x²]
=lim x→+∞x²/[1＋x²]
=lim x→+∞2X/[2X]
=1