极限理论在数学分析中的地位与作用及求极限的方法

Role and Function of Limit in Mathematical Analysis and Ways of Limiting

极限的思想是近代数学的一种重要思想,数学分析就是以极限概念为基础、极限理论(包括级数)为主要工具来研究函数的一门学科。所谓极限的思想,是指用极限概念分析问题和解决问题的一种数学思想。用极限思想解决问题的一般步骤可概括为:对于被考察的未知量,先设法构思一个与它有关的变量,确认这变量通过无限过程的结果就是所求的未知量;最后用极限计算来得到这结果。

As an important idea of modem mathematics, mathematical analysis is a subject that is based on the concept of limit and use limit theory （including the series） as the main tool to study the function. The so - called limits refers to a mathematical idea using the concept of limit analysis to analysis and solve problems, the general steps toselve problems by limiting can be summarized as follows： For an unknown quantity to be assessed, first try to thing of a variable associated with it, confirm the result of a variable after the endless process is the quantity and then get the result by limiting.