| 微分中值定理的另类证明与应用 |
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| 引用本文： | 王秀玲.微分中值定理的另类证明与应用[J].安庆师范学院学报(自然科学版),2010,16(4):93-95. |
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| 作者姓名： | 王秀玲 |
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| 作者单位： | 宿迁高等师范学校,数学系,江苏,宿迁,223800 |
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| 摘 要： | 在通常的数学分析教材中,微分中值定理的证明是通过构造辅助函数,在罗尔中值定理的基础上证明的。受到Darboux定理的证明方法的启发,本文给出了构造另类辅助函数,应用罗尔中值定理证明微分中值定理的新方法,并介绍了微分中值定理在解决数学问题中的广泛应用。
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| 关 键 词： | 微分中值定理 Darboux定理 辅助函数 |
The Different Proofs of the Differential Mean Value Theorem and Its Application |
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| WANG Xiu-ling.The Different Proofs of the Differential Mean Value Theorem and Its Application[J].Journal of Anqing Teachers College(Natural Science Edition),2010,16(4):93-95. |
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| Authors: | WANG Xiu-ling |
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| Institution: | WANG Xiu-ling(Department of Mathematics,Suqian Higher Normal School,Suqian 223800,China) |
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| Abstract: | In the general mathematical analysis textbooks,the proof of the differential mean value theorem is built on the Rolle's theorem by means of constructing an auxiliary function.Inspired by the proof of Darboux Theorem,this paper gives two new ways to prove the Lagrange Mean Value and the Cauchy Mean Value Theorem where two different auxiliary functions are constructed and the Rolle's theorem is applied.Furthermore one introduces some application of the differential mean value theorems in solving mathematical ... |
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| Keywords: | differential mean value theorem Darboux theorem auxiliary function |
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