关于特殊二元函数极限的讨论  

On the Limit of Special Binary Function

作　　者：周香孔[1] 宋根壮[2] 

机构地区：[1]衡水学院数学系,河北衡水053000 [2]衡水学院教务处,河北衡水053000

出　　处：《衡水学院学报》2005年第1期3-4,共2页Journal of Hengshui University

摘　　要：由一元函数f(x)在点x0 的极限存在,很容易地得出特殊二元函数F(x,y) =f(x)在点(x0,y0 )的二重极限也存在。但若limx→x0f(x) =A,f(x)在x0 有意义,且f(x0 )≠A,则二重极限limx→x0f(x)不存在.From the existence in x_0 of the limit of the function f(x), it is easy to conclude that there is the existence of the dual limit in (x_0,y_0) of the special binary functionF(x,y)=f(x). But if limf(x)=A, there is a definite point in x_0 of F(x) and if f(x_0)≠A,then there is no dual limit of (lim)(x→x_0)(y→y_0)f(x).

关 键 词：函数 极限 二重极限 

分 类 号：O171[理学—数学]