摘要
文[1]、[2]对一元函数微分中值定理“中间点”的渐近性进行了讨论,获得了成果。本文把这种讨论推广到多元函数的拉格朗日中值定理及柯西中值定理中去,得到了更普遍的结果。主要结果有两个:当动点x_0+h趋向于x_0点时,限定“中间点”取在x_0、x_0+h的连线段内,在很宽的条件下,有当动点x_0+h依某确定方向趋近于x_0点时,可以证明(见引理)在很宽的条件下,存在着不在x_0与x_0+h连线上的“中间点”,中间点可以依另一个确定的方向趋近于x_0。
In this paper the asymptotic behavior of intermediate points is discussed for the differential mean value theorem of functions of several variables, and general results are obtained.The main results are as follows:whenAs the moving point x0+h tends to x0 along a certain direction, these are 'inter mediate point' ξ not belonging to the joining line of x0 and x0+h, and ξ tends to x0 along another define direction, In this case,
出处
《北京建筑工程学院学报》
1995年第2期16-31,共16页
Journal of Beijing Institute of Civil Engineering and Architecture
关键词
多元函数
中值定理
渐近性
微分
Derivative of Fre'chet
intermediate pomt
along a certain direction
