作者midarmyman (midarmyman)
看板trans_math
标题Re: 一题极限
时间Mon Apr 12 20:13:13 2010
※ 引述《wj1 (wj01)》之铭言：
: 2 2
: x - sin x
: lim ------------- = ?
: n->无限 2 2
: x sin x
:
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 140.117.198.78
1F：推 math1209:你的分母是 0 if x = k(pi). 展开後, 依 114.32.219.116 04/12 20:20
2F：→ math1209:然是 0. 114.32.219.116 04/12 20:20
3F：→ mmmaaatttttt:这不能用次方比大小吧，上下都是无穷 111.250.192.93 04/12 20:21
4F：→ math1209:换言之, 跟展不展开没什麽关系 = = 114.32.219.116 04/12 20:22
5F：→ midarmyman:分母是零? 不懂 140.117.198.78 04/12 20:32
6F：→ midarmyman:分子分母同除分子的最高次 140.117.198.78 04/12 20:32
7F：推 math1209:分母部分为 x^2 sin^2 x = g(x). 114.32.219.116 04/12 20:32
8F：→ midarmyman:分母的次方不是一定比较大? 140.117.198.78 04/12 20:33
9F：→ math1209:只要 x = k(pi), g(x) 都是 0. 114.32.219.116 04/12 20:33
10F：→ math1209:即使你将 sin^2 x 展开写为 h(x) = ... 114.32.219.116 04/12 20:33
11F：→ math1209:你的分母还是 x^2 h(x) = g(x). 114.32.219.116 04/12 20:33
12F：→ math1209:注意, 等号在数学上可是很强的条件... 114.32.219.116 04/12 20:33
13F：→ math1209:简单的说, 定义 h(x) = sin^2 x. 114.32.219.116 04/12 20:34
14F：→ math1209:即使你将 h(x) 写成 Taylor 展开 114.32.219.116 04/12 20:35
15F：→ math1209:他依然得满足 h( k (pi) ) = 0 . 114.32.219.116 04/12 20:35
16F：→ midarmyman:懂你意思! 还是要照原函数来看比较准QQ 140.117.198.78 04/12 20:35
17F：→ midarmyman:那我let x=1/t再展开 不就行了? 140.117.198.78 04/12 20:38
18F：→ midarmyman:就是零 颗颗 140.117.198.78 04/12 20:38
※ 编辑: midarmyman 来自: 140.117.198.78 (04/12 22:51)
19F：推 keith291:non well-defined 61.216.60.19 04/12 23:24
20F：→ keith291:取n=kπ,n→∞ as k→∞ 此时即限不存 61.216.60.19 04/12 23:26
※ 编辑: midarmyman 来自: 140.117.198.78 (04/12 23:46)