二元函数高阶Cauchy中值定理“中间点”的渐近性  

Asymptotic Behavior of “Intermediate Point” in the High Order Cauchy Mean Value Theorem for Two Variable Functions

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

机构地区：[1]渤海大学数理学院,辽宁 锦州 121013

出　　处：《北华大学学报（自然科学版）》2020年第1期1-6,共6页Journal of Beihua University（Natural Science）

基　　金：国家自然科学基金项目(11371070);渤海大学研究生创新基金项目(YJC20170036)

摘　　要：研究二元函数高阶Cauchy中值定理"中间点"(x0+θΔx,y0+θΔy),当点B(x0+Δx,y0+Δy)沿BA连线趋向于点A(x0,y0)时的渐近性态,利用比较函数概念,在一定条件下建立了二元函数高阶Cauchy中值定理"中间点"(x0+θΔx,y0+θΔy)的几个渐近估计式.The purpose of this paper is to study asymptotic behavior of the "intermediate point"(x0+ θΔx,y0+θΔy) in the high order Cauchy mean value theorem for two variable functions when pointB(x0+Δx,y0+Δy)approaches pointA(x0,y0) along line segmentBA, by using the concept for comparison function, asymptotic estimation formula of the "intermediate point"(x0+ θΔx,y0+ θΔy) in the high order Cauchy mean value theorem for two variable functions is established under certain conditions.

关 键 词：比较函数 二元函数高阶Cauchy中值定理 中间点 洛必达法则 

分 类 号：O172.1[理学—数学]