![](https://iknow-base.cdn.bcebos.com/lxb/notice.png)
请大神帮忙解一下这道题
1个回答
展开全部
解:
lim [√(x²+1)-√(x²-1)]
x→∞
=lim [√(x²+1)-√(x²-1)][√(x²+1)+√(x²-1)]/[√(x²+1)+√(x²-1)]
x→∞
=lim [(x²+1)-(x²-1)]/[√(x²+1)+√(x²-1)]
x→∞
=lim 2/[√(x²+1)+√(x²-1)]
x→∞
=lim (2/x)/[√(1+ 1/x²)+√(1- 1/x²)]
x→∞
=0/[√1+0)+√(1-0)]
=0/2
=0
lim [√(x²+1)-√(x²-1)]
x→∞
=lim [√(x²+1)-√(x²-1)][√(x²+1)+√(x²-1)]/[√(x²+1)+√(x²-1)]
x→∞
=lim [(x²+1)-(x²-1)]/[√(x²+1)+√(x²-1)]
x→∞
=lim 2/[√(x²+1)+√(x²-1)]
x→∞
=lim (2/x)/[√(1+ 1/x²)+√(1- 1/x²)]
x→∞
=0/[√1+0)+√(1-0)]
=0/2
=0
推荐律师服务:
若未解决您的问题,请您详细描述您的问题,通过百度律临进行免费专业咨询