基本初等函数极限的新讲法

New Teaching Method of Limits of the Basic Elementary Functions

基本初等函数的极限是微积分中重要的教学内容,然而由于高职院校学生的数学基础普遍较差,这给教学带来了巨大挑战。文章提出了讲授基本初等函数极限的新思路:首先,基于幂函数对极限概念进行初步讲授;其次,给出基本初等函数极限的思考方法,并分别对指数函数、三角函数、对数函数以及反三角函数给出各种情况的极限;最后,给出基本初等函数极限的汇总表。

The limit of basic elementary function is an important part of calculus teaching.However,because of the general poor mathematical foundation of the students in higher vocational colleges,this brings a great challenge to the teaching.The article puts forward a new idea to teach the limits of basic elementary functions.Firstly,the limit concept is given a preliminary instruction based on the power function.Secondly,the thinking method of limits of the basic elementary functions is given,and the limits of the exponential function,trigonometric function,logarithmic function and inverse trigonometric function are given respectively.Finally,a summary of limits of the basic elementary functions is given.