lim [e^(lnx /x)-1] / x^(-1/2) x趋近于正无穷

题目

lim [e^(lnx /x)-1] / x^(-1/2) x趋近于正无穷

答案

lim lnx /x =lim((1/x)/1)=0
e^t-1~t t->0 等价无穷小代换
lim [e^(lnx /x)-1] / x^(-1/2)
=lim [(lnx /x)] / x^(-1/2)
=lim (lnx /x^(1/2)
=2lim (1/x^(1/2)
=0