lim(x→∞)x[ln(x-1)-lnx]

问题描述:

lim(x→∞)x[ln(x-1)-lnx]

lim(x→∞)x[ln(x-1)-lnx]=lim(x→∞)ln(((x-1)/x)^x)=lim(x→∞)ln((1-1/x)^x)
令-1/x=t,则x=-1/t代入上式得:ln(lim(x→∞)(1+t)^(-1/t))=ln(1/e)=-1