关于分段函数相关问题的教学探讨  

Induction in teaching about related problems of segmented function

作　　者：马艳丽[1] 潘娟娟[1] 褚正清[1] 李海霞[1] 

机构地区：[1]安徽新华学院公共课教学部,安徽合肥230088

出　　处：《佛山科学技术学院学报（自然科学版）》2016年第6期37-43,51,共8页Journal of Foshan University(Natural Science Edition)

摘　　要：函数是高等数学的主要研究对象,其中分段函数是一类非常特殊且具有代表性的函数,它是数学教学中的重点,同时也是学生不易掌握的难点。通过具体实例分析了分段函数的极限、连续性、导数、积分和极值的求法以及容易出现的问题,指出理解分段函数有关内容的关键是掌握其在分界点处的特殊变化。Function is the main research object in higher mathematics. Segmented function is a kind of very special and representative function. It is the key point in mathematics teaching, and also the difficulty point which is not easy for students to learn. The limit, the derivative, the integral and the extreme value of the segmented function at the boundary point are the more difficult contents for the students. This paper analyzed the method and problems of the limit, the continuity,the derivative, the integral and the extreme value of the segmented function by giving some examples,and pointed out that the key to understanding the segmentation function is to master the special changes in the boundary points, which helps the deep understanding and comprehension.

关 键 词：分段函数 连续性 导数 积分 极值 

分 类 号：O174[理学—数学]