紧急求助lim(x→无穷大）e^x/(x2+lnx)

题目

紧急求助lim(x→无穷大）e^x/(x2+lnx)

答案

两次应用罗比达法则,分子分母同时求导
lim(x→无穷大）e^x/(x^2+lnx)=lim(x→无穷大）e^x/(2x+1/x)=lim(x→无穷大）e^x/(2-1/x^2)=无穷