n趋于无穷,n^2/(e的根号下n次方)的极限怎么算?

Question

n趋于无穷,n^2 / (e的根号下n次方)的极限怎么算?

Answer 1

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^√n
n趋于无穷,所以极限等于0