62问答网 > 求极限:lim(2n∧3-3n^2 n 2)⼀(3n^3+2n-1) n趋于无穷

求极限:lim(2n∧3-3n^2 n 2)⼀(3n^3+2n-1) n趋于无穷

lim(2n∧3-3n^2+n+2)⼀3n^3+2n-1 n趋于无穷

2025-06-20 15:08:19

推荐回答（1个）

回答1：

用N-ε语言
对于任意ε>0
存在N=max(1,5/2ε)
当n>N时
|(3n^2+n)/(2n^2-1)-3/2|
=|(6n^2+2n-6n^2+3)/[2(2n^2-1)]|
=(2n+3)/[2(2n^2-1)]
因为n>N>=1,所以2n+3<2n+3n=5n
2n^2-1>2n^2-n^2=n^2
(分子更大,分母更小的数更大)
<5n/[2(n^2)]
=5/2n
<5/2(5/2ε)
=ε
由极限定义
lim n->∞ (3n^2+n)/(2n^2-1)=3/2