1、共 17 页 第 1 页 浅谈函数极限求解方法浅谈函数极限求解方法 摘要：摘要： 极限是数学分析的基础，数学分析的基本概念的表述，都可以用极限来描述.如函 数在某点处导数的定义,定积分的定义,偏导数的定义,二重积分的定义,三重积分的定义,无穷 级数的定义都是用极限来定义的.极限是研究数学分析的基本工具.极限是贯穿数学分析的一 条主线.学好极限要从以下两个方面着手: 1)是考察所给函数是否存在极限;2）若函数存在极 限,则考虑如何计算此极限.本文主要是对第二个问题即在极限存在的条件下,如何去求极限 进行综述. 对于简单的极限的计算，利用定义求值或利用极限的四则运算法则求值都是 可 行的,但是对于
2、一个比较复杂的极限的计算,例如的值时 则不能直接采用一般的定义或者定 理，即使采用洛必达法则也是比较繁琐的,然而用泰勒展示则计算简单多了,这就说明为一般 地解决极限求值问题时,就必须利用有效有针对性的计算方法，对各个具体问题还要善于发 现和利用其特点以简化手续 传统的极限的计算方法不下十几种,但具体到计算不同特征 的极限时,究竟采用哪种方法,很多人总感到无从下手只有将这些方法进行归纳总结,从而才 可以针对不同特征的式子选择适当的计算方法,进而简化计算 Abstract： Limit is the basis of mathematical analysis , the basic concep
3、ts of mathematical analysis of expression , can be used to describe the limit as a function definition derivative at some point , the definition of the definite integral , the definition of partial derivative , the definition of double integrals , triple integral definition , infinite series of defi
4、nitions are used to define the limits of the limit is the basic tool to study the limits of mathematical analysis is a main theme throughout the mathematical analysis to learn the limits from the following two aspects is to investigate the function if there is a limit .If there is a limit function ,
5、 then consider how to calculate this limit this article is the second question that under the conditions of the existence of the limit , how to find the limits are reviewed for a simple calculation of the limit of the use . define the limits of the evaluation or the use of four evaluation algorithms
6、 are feasible, but for a more complicated limit calculations, such asFind in coslimx when exxx values are not directly using the general definition or theorem, even with the Hospitals Rule is more complicated , however, Taylor shows the calculation is much simpler , which is generally described when the limit is evaluated to solve the problem , we must use effective targeted method of calculation for each specific issues but also good at finding and using its features to simplify procedures.
