n趋于无穷,n^2 / (e的根号下n次方)的极限怎么算?

题目

n趋于无穷,n^2 / (e的根号下n次方)的极限怎么算?

答案

用洛必达法则n^2/e^√n上下求导=2n/[e^√n*(1/2√n)]=4n√n/e^√n=4n^(3/2)/e^√n再求导=6n^(1/2)/[e^√n*(1/2√n)]=12n/e^√n再求导=12/[e^√n*(1/2√n)]=24√n/2/e^√n再求导=24*(√n)'/[e^√n*(√n)']=24/e^√nn...