Study on some common methods for function limit
函数极限的几类常见求解方法探析

摘要

函数极限计算是高等数学教学中的一类重要问题，是函数微积分学研究的基础，理解并灵活运用极限的各种计算方法对学好高等数学至关重要。由于极限类型和求解方法的多样性，很多学生无法很好地掌握每种方法的适用条件和使用技巧，导致做题时无从下手。如何帮助学生掌握函数极限，特别是未定式极限的求解方法是高等数学教学中的重点和难点。针对该问题，由于大部分未定式极限题都可通过转化为0/0型求解，故本文以一道0/0型未定式极限题为例，总结并详细分析了几类求解函数极限的常见方法及其适用条件和关键步骤，以此帮助学生熟练掌握极限计算方法，并培养学生的发散思维能力。

Abstract

Function limit calculation is an important problem in advanced mathematics teaching and the basis of function calculus research. Understanding and flexibly applying various limit calculation methods is crucial to learning advanced mathematics. Due to the diversity of limit types and solution methods, many students cannot master the applicable conditions and usage skills of each method well, resulting in a lack of knowledge when doing questions. How to help students master function limits, especially the solution methods of indeterminate limits, is the key and difficulty in advanced mathematics teaching. In response to this problem, since most indeterminate limit problems can be solved by converting them into 0/0 type, this paper takes a 0/0 type indeterminate limit problem as an example, summarizes and analyzes in detail several common methods for solving function limits and their applicable conditions and key steps, so as to help students master limit calculation methods and cultivate students' divergent thinking ability.