关于二元函数可微的若干条件的质疑  

Questions on Some Conditions for the Differentiability of Functions of Two Variables

作　　者：蔡希晨 施可心 CAI Xichen;SHI Kexin(School of Mathematics and Statistics,Fujian Normal University,Fuzhou 350117,China)

机构地区：[1]福建师范大学数学与统计学院,福建福州350117

出　　处：《高等数学研究》2025年第2期35-37,共3页Studies in College Mathematics

基　　金：福建师范大学2023年大学生创新创业训练计划项目资助。

摘　　要：本文对二元函数可微性的若干充分条件、必要条件及其证明提出质疑,给出反例说明这些条件不成立,并深入分析其证明错误的原因.This paper examines the validity of certain sufficient and necessary conditions for the differentiability of functions of two variables.Counterexamples are provided to demonstrate the failure of these conditions,and the underlying flaws in their proofs are thoroughly analyzed.

关 键 词：可微性 偏导数 LAGRANGE中值定理 

分 类 号：O174[理学—数学]