lim（x→∞）[x-(x^2)ln(1+1/x)] (t=1/x,t→0)=lim（t→0）[1/t-ln(1+t)/t^2] =lim（t→0）[t-ln(1+t)]/t^2=lim（t→0）[1-1/(1+t)]/(2t)=lim（t→0）t/[(1+t)(2t)]=1/2
