用代换法求解二重极限的类型和实例

The Types and Examples to Seek the Solution to Double Limit with the Substitution Technique

对于二元函数的二重极限,重点是极限的存在性及其求解方法.由于二重极限较为复杂,判定极限的存在及求解,往往因题而异.依据变量(x,y)的不同变化趋势和函数f(x,y)的不同类型,探索得出了一些新的变量代换及应用.采用恰当的变量代换的求解方法后,对复杂的二重极限计算,就能简便、快捷地获得结果.

For double limit of a binary function, the existence of the limit and the methods to seek its solution are emphasis among our focus. As the double limit is complex, to discriminate the existence of the limit and to seek its solution are different. According to the dissimilar change trend and the different function types, some new variable substitutions and application are found out in this paper. Then, after a number of double limits reckoned, the results could be obtained simply and swiftly with the suitable variable substitutions.