第一个重要极限的几种证明及其应用

The first of several important limit its application to prove

第一个重要极限lim x→0=sinx/x=1是高等数学极限知识中较为重要的知识点之一,这个极限对我们学习其他数学知识都有着非常重要的帮助。文章主要介绍这个极限的几种证明方法,以加深对其的了解,并介绍它在极限计算、导数公式推导、近似计算和数列级数极限计算中的应用。

The important limit formula:lim x→0 =sinx/x=1 is one of the important knowledge in higher mathematics,and it is very useful for us to gain other knowledge.In this paper,I will introduce several methods to prove this limit.Moreover,I will present the applications of it in limit calculation,derivative formula derivation,and approximate calculation and limit calculation of sequence series.