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求极限是高等数学中最基本的运算之一,它在现行中学数学教学中也占有重要地位。本文按统编教材的有关内容(全日制十年制高中数学第四册第七章),对极限计算的常用方法做一点归纳,供中学生学习参考。一、依函数的连续性求极限中学数学中所讨论的函数是初等函数,而初等函数在其定义域内都是连续的,因此根据函数连续的定义,求连续函数的极限值可变为求在给定点处的函数值。
The limit is one of the most basic operations in higher mathematics. It also occupies an important position in the current middle school mathematics teaching. This article summarizes the common methods of limit calculation for the reference of middle school students according to the relevant contents of the textbook (the seventh chapter of full-year ten-year high school mathematics fourth volume). First, according to the continuity of the function of the limit of high school mathematics discussed in the function is an elementary function, and elementary functions are continuous in the definition of the domain, so according to the definition of continuous function, the limit of the continuous function can be changed to be in The function value at a given point.