推广的中值定理再推广的一个注记  

A Note on the Generalization of the Generalized Mean-Value Theorem

作　　者：涂振坤[1] 时军[1] TU Zhenkun;SHI Jun(School of Mathematics,Hefei University of Technology,Hefei 230601,China)

机构地区：[1]合肥工业大学数学学院,合肥230601

出　　处：《大学数学》2024年第6期92-97,共6页College Mathematics

基　　金：安徽省省级教学研究项目(2023jyxm0058,2021jyxm1190);合肥工业大学课程思政精品示范课程(KCSZ2022007);合肥工业大学创新创业教学改革研究项目(JYCX2209)。

摘　　要：在高等数学教学中常涉及微分中值定理,将这些微分中值定理进行推广具有一定意义.本文指出文献[10]存在的两个错误,用更简便的方法证明其定理,并给出几个相关不等式.In advanced mathematics education,differential mean value theorems are often covered and it is a meaningful topic to extend these theorems.This paper points out two errors in literature[10],proves its theorem by a simpler method,and gives several related inequalities.

关 键 词：TAYLOR中值定理 CAUCHY中值定理 n+1阶导数 不等式 

分 类 号：O177.5[理学—数学]