设二元函数f(x,y),P_o(x_o,y_o)为定义域D中一个聚点,A是一个确定的实数。若对Aε>0,Eδ>0,当p(x,y)∈v~0(p_o,δ)D时,有|f(x,y)-A|<ε,则称A是f(x,y)在P_o点的(二重)极限。记作lim f(x,y)=A或lim f(x,y)=A.(x,y)→(x_o,y_o) x→x_o y→y_o 例如,讨论xy~2/x~2+y~4在(0,0)点的极限。 设f(x,y)= xy~2/x~2+y~4,令y=0,则f(x,0)=0,(x≠0)即当P(x,y)沿x轴趋于(0,0)点时,f(x,y)→0, Let the binary function f(x,y), P_o(x_o,y_o) be an aggregation point in the domain D, and A is a definite real number. If Aε>0, Eδ>0, when p(x,y)∈v~0(p_o,δ)D, there is |f(x,y)-A|<ε, then A is said to be f(x). , y) The (double) limit at the P_o point. Let lim f(x,y)=A or lim f(x,y)=A.(x,y)→(x_o,y_o) x→x_o y→y_o For example, discuss xy~2/x~2+ The limit of y~4 at the (0,0) point. Let f(x,y)=xy~2/x~2+y~4, let y=0, then f(x,0)=0, (x≠0) ie when P(x,y) is along the x When the axis goes to (0,0) point, f(x,y)→0,