洛必达法则在高中数学中的应用探究

Exploring the Application of Lopita’s Law in High School Mathematics

摘要: 随着新课标在全国范围内的实施，具有高观点知识背景的题目在高考中所占比例越来越大了。已知不等式恒成立求参数的取值范围作为高考重点考查的题型之一，综合难度大，对学生的思维水平要求高。倘若学生能采用洛必达法则处理该类问题可以直击问题命脉，提高解题效率。鉴于目前许多学生对洛必达法则的理解存在偏差，以高考真题为例分析了法则应当如何合理应用，设计了法则融入高中数学的教学设计，希冀为一线教育教学提供参考。

Abstract: With the implementation of the new standards across the country, questions with a high viewpoint knowledge background are taking up a larger and larger proportion of the GCE. As one of the key questions in the HKALE, the range of values of the parameter for which the inequality is known to be constant is difficult to synthesise and requires a high level of student thinking. If students can use Lopita’s Law to deal with this type of problem, they can get straight to the heart of the matter and improve their efficiency. In view of the current bias of many students in understanding Lopita’s Law, we have analysed how the Law should be applied rationally, using real questions from the HKALE as examples, and designed a teaching design for the integration of the Law into high school mathematics, with the hope of providing reference for front-line education and teaching.