一类单调有界连续可微函数的导函数极限问题  

Derivative Functions’Limit Problems for Monotone,Bounded and Continuously Differentiable Functions

作　　者：毛俊杰 刘晓薇[1] MAO Jun-jie;LIU Xiao-wei(School of Mathematics and Statistics,Qilu University of Technology (Shandong Academy of Sciences),Jinan250353,China)

机构地区：[1]齐鲁工业大学(山东省科学院)数学与统计学院,济南250353

出　　处：《齐鲁工业大学学报》2019年第3期79-80,共2页Journal of Qilu University of Technology

基　　金：国家自然科学基金(11601251).

摘　　要：本文基于文献给出的反例,知道了并不是所有单调有界且连续可微函数在x→时导函数的极限都为0。并且基于本文的定理,给出了能证明单调有界且连续可微函数在x→时导函数极限为0的两个充分条件。Based on the counterexample given in literature,it is known that not all derivative functions of monotone,bounded and continuously differentiable functions have a limit of 0 when x→∞.Based on the theorem of this paper,two sufficient conditions are given to prove that the derivative functions of monotone,bounded and continuously differentiable functions have a limit of 0 when x→∞.

关 键 词：导函数 极限 一致连续 

分 类 号：O29[理学—应用数学]