Question

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极限思想指从有限认识无限的思想方法。某些问题若着眼于问题的极限状态，灵活地借助极限思想解题，则可避免抽象及复杂的运算，降低解题难度，优化解题思路。极限的本质-----既是无限的过程，又是确定的结果。极限理论有高度的抽象性、广泛的应用性和普遍的指导性。数学分析是大学本科数学专业的基础课程，数学分析这门课程研究的对象是函数,而研究函数方法就是极限,数学分析中几乎所有的概念都离不开极限，如连续、导数、定积分等都是由极限定义的，它将数学分析的各个知识点连在了一起。而极限运算是数学分析的基本运算。于是，我们非常有必要针对性地去探索求极限值的若干方法，对数学分析中求极限值问题的理论研究和应用实践都具有有价值的重要意义。
求极限的方法很多，而且非常灵活，因此研究与总结求极限的方法尤为重要。本文在原有知识体系的基础上加以整理和归纳，针对各种形式的极限概括出若干主要方法，并配以代表性的例题来诠释方法的适用性和典型性，力求达到对原有知识的巩固和提高的目的，进而对数学分析这门课程以及后续课程有更深入的体会和理解。

Answer 1

Extreme thought from the limited knowledge of infinite thinking methods. If some problems on the limit state and problems flexibly by solving extreme thought, can avoid abstract and complex operation, reduce the difficulty of solving optimization problem solving and ideas. Limit the nature - - - - - is infinite, and determine the outcome. Limit theory has high abstraction, widely applied and general guidance. Mathematical analysis is undergraduate professional basic course of mathematics, the mathematical analysis, this course of study object, and study is the function is the limit function method, mathematical analysis in almost all of the concept of limit, as all continuously and derivative, integral is defined by the limits of mathematical analysis, it will be all knowledge together. But limit is the basic mathematical analysis. So, we are very necessary to explore for pertinently the limit of some methods of mathematical analysis, ask questions related to the theoretical research and practical application has important significance of value.
The limit of the method are many, and very flexible, so study and summarizes the method is particularly important to the limit. Based on the existing knowledge system basis and classified, according to various forms of several main methods limit summarized, and the method of representative examples to explain the applicability and typicality, strive to achieve the original knowledge to stabilize and improve the purpose of mathematical analysis, this course and the subsequent courses more experience and understanding.