关于三类基本初等函数的拉格朗日中值点的渐近性  

On the Asymptotic Property of the Mediate Point in the Lagrange’s Mean Value Theorem of Three Basic Elementary Functions

作　　者：张传芳 杨春玲 

机构地区：[1]广东石油化工学院理学院,广东 茂名

出　　处：《理论数学》2023年第10期2737-2743,共7页Pure Mathematics

摘　　要：本文讨论了三种基本初等函数的拉格朗日中值点的渐近性问题,结果表明:除幂函数当区间左端点为0时,中值取定值外,其余情况的幂函数、指数函数、对数函数当区间右端点趋向于区间左端点时,拉格朗日中值点均趋向于区间中点。In this paper, the asymptotic behavior of the Lagrange median points of three basic elementary functions is discussed. The results show that, except for the power functions where the left endpoint of the interval is 0 and the median value is fixed, the power functions, exponential functions, and logarithmic functions of median points tend to the midpoint of the interval, when the right endpoint of the interval tends to the left endpoint.

关 键 词：渐近性 中值点 拉格朗日中值定理 基本初等函数 

分 类 号：O17[理学—数学]