lim(x→∞)x(π-2arctanx）
=lim(x→∞)(π-2arctanx）/(1/x)
[洛必达法则]
=lim(x→∞)[0-2/(1+x^2)]/(-1/x^2)
=lim(x→∞)2x^2/(1+x^2)
=lim(x→∞)2/(1+1/x^2)
=2/(1+0)
=2