柯西微分中值定理的一个新的证明方法  

A NewMethod to prove Couchy' s Theorem of Mean for Derivatives

作　　者：陈蕴衡[1] 郭正光[2] 

机构地区：[1]山西财经学院 [2]太原重型机械学院

出　　处：《太原重型机械学院学报》1991年第2期53-58,共6页Journal of Taiyuan Heavy Machinery Institute

摘　　要：本文通过构造一个新的函数,得到了两个点列,从而获得了柯西微分中值定理的一个新的证明方法。而拉格朗日微分中值定理和罗尔微分中值定理既可以作为两个推论给出,也可以根据本文提供的方法直接证明。这种方法完全区别于一般数学分析教科书中有关微分中值定理的证明方法,从而具有一定的参考价值。This paper demonstrates that two ranges of points have been obtained through building a new function, and as a result, a new method to prove Cauchy's Theorem of Meean for Derivatives has been arrived at Therefore Lagrange's Theorem of Mean for Derivatives and Rolle's Theotrem of Mean for Derivatives can either be given as two inferences, or be directly proved with the method provided in this paper,This method is' totally ditferent from the those methods in common analytical text books of mathematics, and this method has certain value for reference.

关 键 词：柯西微分 中值 定理 点列 区间套 

分 类 号：O172.1[理学—数学]