求lim(x→∞)x(e^1/x-1)的极限,

题目详情

求lim(x→∞) x(e^1/x-1)的极限,

▼优质解答

答案和解析

lim(x→∞) x(e^1/x-1)
=lim(x→∞) [(e^1/x-1)/(1/x)]
=lim(x→∞) (e^1/x-1)'/(1/x)'
=lim(x→∞) [e^(1/x)](-1/x^2)/(-1/x^2)
=lim(x→∞) e^(1/x)
=e^0
=1

看了求lim(x→∞)x(e^1...的网友还看了以下：