| Lagrange中值定理“中间点”的渐进性 |
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| 引用本文： | 帅雁丹.Lagrange中值定理“中间点”的渐进性[J].渝州大学学报(自然科学版),2009(5):437-438. |
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| 作者姓名： | 帅雁丹 |
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| 作者单位： | 重庆师范大学数学与计算机科学学院,重庆401331 |
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| 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limb→a ζ-a/b-a=m√1/m＋1.
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| 关 键 词： | Lagrange中值定理 中间点 渐进性 |
Research into progressiveness of intermediate point of Lagrange mean value theorem |
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| SHUAI Yan-dan.Research into progressiveness of intermediate point of Lagrange mean value theorem[J].Journal of Yuzhou University(Natural Sciences Edition),2009(5):437-438. |
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| Authors: | SHUAI Yan-dan |
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| Institution: | SHUAI Yan-dan (School of Mathematics and Computer Science, Chongqing Normal University, Chongqing 401331 ,China) |
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| Abstract: | This paper makes qualitative research on the progressiveness of the intermediate point of Largrange mean value theorem. By studying the situation of f（x） 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：limb→a ζ-a/b-a=m√1/m＋1. |
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| Keywords: | Lagrange mean value theorem intermediate point progressiveness |
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