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| 柯西中值定理的证明与应用 | |
| 引用本文： | 张跃平,葛健芽,沈利红.柯西中值定理的证明与应用[J].金华职业技术学院学报,2006,6(3):57-60. |
| 作者姓名： | 张跃平 葛健芽 沈利红 |
| 作者单位： | 1. 浙江师范大学,数理学院,浙江,金华,321004 2. 金华职业技术学院,浙江,金华,321007 3. 同济大学,应用数学系,上海,200433 |
| 摘 要： | 本文介绍了柯西中值定理的多种证明方法及其应用.其中证明方法有:利用构造辅助函数,根据罗尔定理证明;利用坐标旋转变换证明;利用达布定理证明;利用复合函数证明;利用同增量性证明.其应用方面为:求极限;证明不等式;证明等式;证明单调性. |
| 关 键 词： | 柯西中值定理 证明 应用 |
| 文章编号： | 1671-3699（2006）03-0057-04 |
| 收稿时间： | 2005-12-15 |
| 修稿时间： | 2005年12月15 |
The Proof and Application of Cauchy Mean-valueTheorem |
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| ZHANG Yue-ping,GE Jian-ya,SHEN Li-hong.The Proof and Application of Cauchy Mean-valueTheorem[J].Journal of Jinhua College of Profession and Technology,2006,6(3):57-60. | |
| Authors: | ZHANG Yue-ping GE Jian-ya SHEN Li-hong |
| Institution: | 1. College of Mathematics and Physics, Zhejiang Normal University, Jinhua 321004, China; 2.Jinhua College of Profession and Technology, Jinhua 321007 China; 3.Department of Applied Mathematics, Tongji University, Shanghai 200433, China |
| Abstract: | This paper introduces the proof and application of Cauchy mean-value theorem from many angles in every aspect.The proof angles include: on the basis of Luoer theorem;changing the direction of coordinate system;on the basis of Darbou theorem;using the composite function;based on the same increment.The application aspects are: solving the problem of limitation;proving inequality;proving monotonicity;proving unanimously successive. |
| Keywords: | Cauchy mean-value theorem proof application |
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