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。
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.
出处
《株洲师范高等专科学校学报》
2005年第5期42-43,47,共3页
Journal of Zhuzhou Teachers College
关键词
微积分
中值定理
统一证明
推广形式
infinitesimal calculus, intermediate value formula unified demonstration generalized
