用罗必达法则求极限:Lim(x趋1)[x/(x-1)-1/lnx]的极限,

问题描述:

用罗必达法则求极限:Lim(x趋1)[x/(x-1)-1/lnx]的极限,

x/(x-1)-1/lnx
=[xlnx-x+1]/(x-1)lnx
应用洛必达法则
=(lnx+1-1)/[lnx+1-1/x]
=(1/x)/(1/x+1/x^2)
=2