几个典型例子在微积分(数学分析)教学中的应用  

On Key Examples in Calculus (Mathematical Analysis) Teaching

作　　者：姚卫红 YAO Weihong(School of mathematics science,Shanghai Jiao Tong University,Shanghai 200240)

机构地区：[1]上海交通大学数学科学学院,上海200240

出　　处：《高等数学研究》2020年第6期45-48,32,共5页Studies in College Mathematics

摘　　要：本文给出并且介绍了几个典型例子在微积分教学当中的应用,其中包括:一、仅在一个点连续且可导的函数,及一种不适用洛必达法则求极限的例子;二、处处可导但导函数却处处不可导的函数;三、用不同的思路构造了一个黎曼可积的函数列收敛到非黎曼可积的函数的例子.In this paper,we construct several examples to support Calculus teaching,including:1)a function which is only continuous and differentiable at one point,and an example that fails the use of L H pital s rule;2)an example of function that is everywhere differentiable but its derivative function is nowhere differentiable;3)an example of a Riemann integrable function sequence converges to a non Riemannian integrable function.

关 键 词：RIEMANN函数 WEIERSTRASS函数 DIRICHLET函数 洛必达法则(L'Hopital's rule) 连续 可导 

分 类 号：O171.1[理学—数学]