化离散为连续的极限求解模型——无穷小和式极限的探究

The Limit Solving Model of Changing the Discrete into Continuous——The Exploration of An Infinitesimal Induces

极限是微积分的基础,对于常规的七类未定型极限,教材都有详细的归类和讲解,对于无数个无穷小和式极限,用常规方法求解比较难,一般教材又不介绍它的极限求解基本方法,而它代表了极限思想的最本质,可用化离散为连续的方法,探究一般的化归模型,并将模型推广,更深层领悟极限的本质,实现离散与连续的熔合。

Limit is the foundation of calculus. The teaching material has a detailed classification and interpretation for the seven conventional undifferentiated limits. For thousands of infinitesimal induces, it＇s difficult to solve by the conventional methods, and the general teaching material do not introduce its basic method to solve the limit,although it represents the essence of limit thought. It＇s available for us to use the method of changing discrete into continuous, and to explore the general reduction model to promote the model. In this way, we can comprehend the essence of limit deeply, and realize the fusion of discrete and continuous.