极限理论是微积分的基础,极限思想是微积分教学过程中的难点.本文在数学应用性教学的背景下,根据极限的未定式类型,对极限的实例模型进行了归纳总结.在大量的极限模型中,体现极限思想的关于无限变化趋势的实例非常多,经典例子如:庄子之锤、芝诺悖论、刘辉割圆术,现代例子如金属加热、室内水温、人口预测、传染病人数、放射物衰减等.在 The limit theory is the basis of the calculus and the limit idea is the difficult point in the teaching of calculus.This paper summarizes the extreme case models according to the undefined types of the limit under the background of mathematical applied teaching.In a large number of limits In the model, there are a lot of examples about the trend of infinity in the limit thinking. The classic examples are Hammer of Zhuangzi, Zeno Paradox, Liu Hui’s circumcision, modern examples such as metal heating, indoor water temperature, population forecast, number of infectious diseases, Radiation attenuation and so on