求极限的若干方法及探讨

Some Methods for Solving the Limit and Discussions

从多个角度讨论了求极限的方法。首先介绍了相对简单的极限的求法,探讨了利用单调有界原理及压缩映像原理求极限和利用Stolz定理求极限。其次是对复合函数求极限,应用Topliz定理的关键在于构造一个Topliz变换得到了特殊的解法,求出复杂函数极限。最后总结了数学分析里求极限的各种方法,得出相应极限的类型、原理,并列举例题。

In this paper we discuss different methods for solving the limit. First we introduce the relatively easier methods of the monotonic bounded principle and the compression image principle and the Stolz theorem to solve the limit. Second, we discuss the methods to solve the limit of a complex function, and we point out that the key to applying the Topliz theorem is to construct a Topliz transformation to obtain a special solution to the limit of a complex function. Based on these, we summarize the various methods for limit solutions in mathematical analysis.Finally, corresponding limit types and principles are concluded, and examples are given.