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

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.