怎么用定义证明呢
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/06/23 23:47:29
怎么用定义证明呢
![](http://img.wesiedu.com/upload/9/12/91284edb3c1009962d440517faec1b2c.jpg)
![](http://img.wesiedu.com/upload/9/12/91284edb3c1009962d440517faec1b2c.jpg)
![怎么用定义证明呢](/uploads/image/z/16212499-43-9.jpg?t=%E6%80%8E%E4%B9%88%E7%94%A8%E5%AE%9A%E4%B9%89%E8%AF%81%E6%98%8E%E5%91%A2)
对任意N>0,当x>N+1时便有
x³/(x²+1)=[x(x²+1)-x]/(x²+1)
=x-x/(x²+1)>N+1-x/(x²+1)
=N+(x²+1-x)/(x²+1)
∵x²+1-x恒>0
∴上式>N
因此原式极限=+∞
x³/(x²+1)=[x(x²+1)-x]/(x²+1)
=x-x/(x²+1)>N+1-x/(x²+1)
=N+(x²+1-x)/(x²+1)
∵x²+1-x恒>0
∴上式>N
因此原式极限=+∞