| 微积分中值定理的统一证明及推广形式 |
| |
| 引用本文： | 刘润辉.微积分中值定理的统一证明及推广形式[J].株洲师范高等专科学校学报,2005,10(5):42-43,47. |
| |
| 作者姓名： | 刘润辉 |
| |
| 作者单位： | 韶关职工大学,广东韶关512031 |
| |
| 摘 要： | Cauchy中值定理统一了微积分中值定理各种形式，从而建立了微分中值定理和积分中值定理之间的内在联系,以Rolle中值定理为基础，借助不同形式辅助函数可对其它几个中值定理作出多种形式的统一证明；利用Taylor公式可以进一步导出微积分中值定理的推广形式。
|
| 关 键 词： | 微积分 中值定理 统一证明 推广形式 |
| 文章编号： | 1009-1432（2005）05-0042-02 |
| 收稿时间： | 06 9 2005 12:00AM |
| 修稿时间： | 2005-06-09 |
Unified Demonstration and Generalization of Intermediate Value Formula in Infinitesimal Calculus |
| |
| Liu RunHui.Unified Demonstration and Generalization of Intermediate Value Formula in Infinitesimal Calculus[J].Journal of Zhuzhou Teachers College,2005,10(5):42-43,47. |
| |
| Authors: | Liu RunHui |
| |
| Abstract: | Cauchy Intermediate Value Formula has unified the diversified intermediate value formulas in infinitesimal and has established the internal relations between integral intermediate value formulas and differential ones. With Rolle Intermediate Value Formula and different assisting functions,some other intermediate value formulas can be demonstrated to be some diversified forms of Cauchy Intermediate Value Formula. Some generalized forms of infinitesimal intermediate value formula can be induced from Taylor Formula. |
| |
| Keywords: | infinitesimal calculus intermediate value formula unified demonstration generalized |
| 本文献已被 CNKI 维普 等数据库收录！ |
