“洛必达法则”使用的常见误区分析与教学对策

Analysis of Common Misconceptions in Using L’Hôpital’s Rule and Teaching Strategies

摘要: 洛必达法则是高等数学中的重点和难点，因其在极限计算过程中的简便而被学生们普遍使用，但是很多学生会因为理解不到位而出现错用和滥用的情况。本文将通过梳理学生在使用洛必达法则过程中出现的常见误区，深入分析误区产生的根源，提出“前提检验、结果判断、未定式辨析、多种方法优化计算”的教学对策，并对此教学对策的教学结果进行了检验。

Abstract: L’Hôpital’s Rule is a key and challenging topic in advanced mathematics. Its simplicity in calculating limits makes it popular among students, yet many misuse or overuse it due to insufficient understanding. This paper systematically examines common misconception students make when applying L’Hôpital’s Rule, delves into the root causes of these misconceptions, and proposes teaching strategies such as “precondition verification, result judgment, identification of indeterminate forms, and optimization of calculations using multiple methods”. The effectiveness of these teaching strategies has also been tested.