第二积分中值定理中值点的唯n性渐近性与可视化  

Exact N-multivaluedness Asymptotic Behavior and Visualization of Mean Value Points in the Second Mean Value Theorem for Integral

作　　者：仉志余 苗雨 ZHANG Zhi-yu;MIAO Yu(Department of Science,Taiyuan Institute of Technology,Taiyuan 030008,China)

机构地区：[1]太原工业学院理学系,山西太原030008

出　　处：《数学的实践与认识》2020年第23期233-243,共11页Mathematics in Practice and Theory

基　　金：山西省自然科学基金(2011011002-3)。

摘　　要：研究第二积分中值定理在本原意义下的中值点存在且唯n(n=1,2,3,…)或充满一个区间的充要条件,得到了一系列新的结果;进而研究多中值点时的渐近性态,所得结果改进和推广了所列文献中的若干结果;最后应用Mathematica和MATLAB数学软件对以上理论结果给出了可视化实例研究.In this paper,based on the original sense of mean value points in the second mean value theorem for integral,the necessary and sufficient conditions for the exact nmultivaluedness(n=1,2,…)or suffusing an interval of the mean value points are studied and a series of new results are obtained.Then the asymptotic behavior of multiple mean value points are discussed and some more generalized conclusions to improve some results of references are drawn.Finally,by using mathematical software,Mathematica and MATLAB,the visualization of the theoretical results are given.

关 键 词：第二积分中值定理 积分中值点 唯一性 唯n性 渐近性 可视化 

分 类 号：O172.2[理学—数学]