论“抓大头”在求极限中的应用

On the Application of “Grasping the Big Head” in Seeking the Limit

高等数学中的一系列重要概念,如函数的连续性、导数以及定积分等都是借助于极限来定义的。正确掌握函数的极限运算方法和运算技巧,对学习好高等数学具有重要意义。本文定义“大头”的概念,给出“大头”的性质和定理,借助于“抓大头”思想解决微积分中一类极限,并通过讲解具有代表性的研究生入学考试真题、大学生数学竞赛题和广东省普通高校本科生招生考试真题,对方法运用加以阐明。

A series of important concepts in higher mathematics, such as the continuity of function, derivative and definite integral, are defined by means of limit. It is of great significance to master the operation methods and skills of function limit for learning higher mathematics. In this paper, the concept of “big head” is defined, the properties and theorems of “big head” are given. With the help of “grasping the big head”, a kind of limit in calculus is solved. The application of the method is il-lustrated by explaining the representative real questions of postgraduate entrance examination, mathematical contest of college students and real problems of undergraduate production entrance examination in Guangdong Province.