| 摘要: |
| 摘 要:对Lagrange中值定理“中间点”的渐进性作了定性研究. 通过对f ( x)在( a, b)内低阶可导情形
的研究,发现规律,即把f ( x)在( a, b)内低阶可导可推广至n阶连续可导的情形,进而把正整数n推广到正
实数m ,并得到了更一般性的结论: lim
b→a
ξ- a
b - a
=
m
1
m + 1
. |
| 关键词: 关键词: Lagrange中值定理 中间点 渐进性 |
| DOI： |
| 分类号: |
| 基金项目: |
|
| Research into progressiveness of intermediatepoint of Lagrange mean value theorem |
|
SHUAIYan2dan
|
| Abstract: |
| Abstract: This papermakes qualitative research on the p rogressiveness of the intermediate point of Largrange
mean value theorem. By studying the situation of f ( ×) in ( a, b) low order derivableness, we found that f ( x) in
( a, b) low order derivative can be popularized to the situation of n order continuous derivableness, furthermore,
that positive integer n can be popularized to positive real number m, a more generalized conclusion is arrived
at: lim
b→a
ξ- a
b - a
m
1
m + 1 |
| Key words: Key words:Lagrange mean value theorem intermediate point p rogressiveness |
