What value does lnx/(x-1) approach as x approaches 1

题目

What value does lnx/(x-1) approach as x approaches 1
What value does lnx/(x-1) approach as x approaches 1

答案

lim (x趋于1) lnx/(x-1)
当x趋于1时,分子lnx,分母x-1均趋于0
应用洛必达法则：分子分母同时求导：
lim (x趋于1) lnx/(x-1)
＝lim (lnx)'/(x-1)'
=lim(1/x)/1
=1/1
=1