等价无穷小代换定理在实际教学中的应用

Application of the Theorem of Equal Infinitesimal Replacement in Practical Teaching

函数的极限,是微积分的研究对象和工具,也是学习高等数学的基础。合理运用等价无穷小代换定理求解函数的极限,可以很大程度简化函数极限的计算过程,相对其他解法,化难为易,使学生容易理解。本文介绍了等价无穷小代换定理,举例说明了应用该定理求解函数极限的优点,分析了教学过程中学生使用该定理遇到的问题,总结了解决的办法。

Limit of a function is the research topic and tool of calculus, and is also the base of learning advanced mathemat-ics. Proper use of the Theorem of Equal Infinitesimal Replacement to get the solution of function, which simplifies maximal-ly the calculation process. Comparing to the other solutions, this method is easier to be accepted by students. This articleintroduces the Theorem of Equal Infinitesimal Replacement, concludes the advantage of using it, analyzes the problems metby the students and summarizes the solutions.