lim(x→+∞)(π/2-arctanx)/sin1/x,

lim(x→+∞)(π/2-arctanx)/sin1/x (0/0型未定式）
=lim(x-->+∞)[-1/(1+x²)]/(-1/x²*cos(1/x)] 【罗比大法则】
=lim(x-->+∞)x²/(1+x²)*1/cos(1/x)
=lim(x-->+∞)1/(1/x²+1)*1/cos(1/x)
=1/(0+1)*1/1
=1