多元函数连续性研究  

Study on the Continuity of Multivariate Function

作　　者：余小飞[1] 李平[1] 

机构地区：[1]河南工业职业技术学院,河南南阳473000

出　　处：《科技创新与生产力》2017年第5期41-42,共2页Sci-tech Innovation and Productivity

摘　　要：笔者根据多元函数连续性的定义,以二元函数连续性为例,研究了多元函数连续性,提出若二元函数的重极限存在,则它沿任何路径的极限都应存在且相等,若某个特殊路径的极限不存在或某两个特殊路径的极限不等,该二元函数就是不连续的,指出三元函数连续性甚至多元函数连续性的研究思路与方法与此相同。The paper studies the continuity of multivariate function taking two-variable function as an example. It points out that if the duplicate limit exists, the limit along any path should exist and be equal, if the limit of a particular path does not exist, or the limits of two particular paths are unequal, the two-variable function is discontinuous. The research ideas and meth- ods on the continuity of three-variable function even multivariate function are the same.

关 键 词：多元函数 连续 极限 特殊路径 

分 类 号：O171[理学—数学]