二元函数柯西中值定理“中间点”的渐近估计式  

ASYMPTOTIC ESTIMATION FORMULA OF THE “INTERMEDIATE POINT” IN THE CAUCHY MEAN VALUE THEOREM FOR TWO VARIABLE FUNCTIONS

作　　者：刘冬红[1] 张树义[1] 郑晓迪 

机构地区：[1]渤海大学数理学院,辽宁锦州121013 [2]锦州师范高等专科学校计算机系,辽宁锦州121000

出　　处：《井冈山大学学报（自然科学版）》2017年第4期13-17,37,共6页Journal of Jinggangshan University (Natural Science)

摘　　要：研究了二元函数柯西中值定理"中间点"(x_0+θ△x,y_0+θ△x),当点B(x_0+△x,y_0+△y)沿AB连线趋向于点A (x_0,y_0)时的渐近性态,利用比较函数概念,在一定条件下证明了二元函数柯西中值定理"中间点"(x_0+θ△x,y_0+θ△x)新的渐近性定理,获得了渐近估计式统一和发展了有关文献中的相应结果。We study asymptotic behavior of the ＂intermediate point＂ （x0＋θ△x,y0＋θ△x）in the Cauchy mean value theorem for two variable functions when point B（x0＋△x,y0＋△y） approaches point A （x0, y0 ） along line segment AB. Based on the concept for comparison function, the new asymptotic behavior theorems of the ＂intermediate point＂（x0＋θ△x,y0＋θ△x）in the Cauchy mean value theorem for two variable functions are proved under certain conditions, we obtain asymptotic estimation formula to unify and extend corresponding results of some reference.

关 键 词：比较函数 二元函数柯西中值定理 中间点 洛必达法则 

分 类 号：O172.1[理学—数学]