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人教A版选修3-1《第五讲 微积分的诞生 三 莱布尼茨的“微积分”》优秀教案设计
5.5 L'H?pital's Rule
Chapter5 Applications of Derivatives
5.5 L'H?pital's Rule
Teaching objectives(教学目标)：
Knowledge and Skills(知识与技能)：
1、Mastering the method and principle of finding the limit of rational functions.掌握有理函数求极限的方法和原理。
2、Understanding the L'H?pital's rule is a method of determining the undetermined value under certain conditions through the molecular and denominator to derive the derivative and then find the limit. It means the limit of the ratio of two infinitesimals or the ratio of two infinitesimals may or may not exist. 理解洛必达法则（L 'H?pital's rule）是在一定条件下通过分子分母分别求导再求极限来确定未定式值的方法。大意为两个无穷小之比或两个无穷大之比的极限可能存在，也可能不存在。
3、Can use L 'H?pital's rule to solve simple mathematical limit problems.能运用洛必达法则解决简单数学极限问题。
Process and methodology（过程与方法）：
Discover and understand the basic ideas of the law with specific examples and master its basic steps.借助具体实例发现并理解洛必达法则的基本思想，掌握它的基本步骤。
Emotional Attitudes and Values（情感态度与价值观）：
Training students in abstract thinking and looking at actual problems with a mathematical eye；
Cultivate students'scientific and rigorous learning attitude.训练学生的抽象思维能力，培养学生用数学的眼光看待实际问题的发生；培养学生科学严谨的学习态度。
By the end of the class, Ss will be able to
1. have a better understanding of how to use L'H?pital's Rule .
2. practice solving the problems of rational functions and express themselves fluently with the Mathematical language.
3. cultivate a proper attitude towards expressing math.
教学亮点Teaching highlights：
1. To explore a story of L'H?pital's Rule，understand the History of Mathematics and Culture.
2. Communicative teaching approach to help students to express math and solve the problems.
教学重难点Teach ing keys and difficulties：
The classification of rational functions, understand the origin and using conditions of the L'H?pital's law, and skillfully use the derivatives and thelaw to solve the limit.
有理函数的分类，了解洛必达法则的由来和使用条件，熟练利用导数和洛必达法则求解极限。
教具Teaching aids：
1. 多媒体The multi-media.