微分中值定理“中间点”的渐近性  

Asymptotic Behavior of "Intermediate Point" for Differential Mean Value Theorem

作　　者：聂辉 张树义[1] 张芯语 NIE Hui;ZHANG Shuyi;ZHANG Xinyu(College of Mathematics and Physics,Bohai University,Jinzhou 121013,China)

机构地区：[1]渤海大学数理学院

出　　处：《南通大学学报（自然科学版）》2019年第3期64-69,共6页Journal of Nantong University(Natural Science Edition)　

基　　金：渤海大学研究生创新基金项目(YJC20170036)

摘　　要：为了研究区间两端点同时趋近于一定点时,柯西微分中值定理"中间点"的渐近性,利用二元函数洛必达法则建立了柯西微分中值定理"中间点"的渐近估计式。与已有文献使用的方法相比,该方法证明过程简练,所得结果新颖,并推广、改进了有关文献中的结果。The purpose of this paper is to study the asymptotic behavior of the "intermediate point" of Cauchy differential mean value theorem when the two ends of the interval approach a certain point at the same time.By using the L’Hospital’s rule of binary function,the asymptotic estimates of the "intermediate point" of Cauchy differential mean value theorem are established.Compared with the previous studies,this paper uses the L’Hospital’s rule of binary function to study its asymptotic behavior,which makes the proof process concise.The results obtained in this paper are original,can improve and extend the corresponding results of some references.

关 键 词：柯西微分中值定理 中间点 渐近性 二元函数洛必达法则 

分 类 号：O171[理学—数学]