| 区间套定理在证明中值定理中的应用 |
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| 引用本文： | 张彩霞.区间套定理在证明中值定理中的应用[J].哈尔滨商业大学学报(自然科学版),2005,21(6):794-796. |
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| 作者姓名： | 张彩霞 |
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| 作者单位： | 大庆石油学院数学系,黑龙江,大庆,163318 |
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| 摘 要： | 对区间套定理给出一个推论,然后建立了四个引理.在此基础上通过构造区间套依次证明了罗尔中值定理、拉格朗日中值定理和柯西中值定理.
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| 关 键 词： | 区间套定理 罗尔中值定理 拉格朗日中值定理 柯西中值定理 |
| 文章编号： | 1672-0946(2005)06-0794-03 |
| 修稿时间： | 2005年8月2日 |
Application of theorem of nested interval in proving mean value theorems |
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| ZHANG Cai-xia.Application of theorem of nested interval in proving mean value theorems[J].Journal of Harbin University of Commerce :Natural Sciences Edition,2005,21(6):794-796. |
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| Authors: | ZHANG Cai-xia |
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| Abstract: | Theorem of nested interval is one of the completeness theorems of real number,it is important in real analysis.This paper gives a corollary of theorem of nested interval and four lemmas.On the basis of these theories,Rolle mean value theorem,Lagrange mean value theorem and Cauchy mean value theorem are proved by constructing nested interval. |
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| Keywords: | theorem of nested interval Rolle mean value theorem Lagrange mean value theorem Cauchy mean value theorem |
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