一种逆用等价无穷小在极限问题中的应用

Application of an Inverse Equivalent Infinitesimal in Limit Problems

极限是高等数学中重要的概念之一,贯穿于高等数学课程的始终,掌握好极限运算是学好高等数学的前提条件,而合理利用等价无穷小是简化极限运算的一种重要方法。针对未定式极限,提出常用等价无穷小“x→0时,x~ln(1+x)”的逆用形式“□→1时,□-1~ln□”,利用该形式能够快速准确地求出一些函数的极限,为解决研究生考试和全国大学生数学竞赛一些极限问题提供重要的方法。

Limit is one of the most important concepts in advanced mathematics throughout.Mastering limit operation is a prerequisite for learning advanced mathematics,and rational use of equivalent infinitesimal is an important method to simplify limit operation.For the indeterminate limit,the inverse form","of equivalent infinitesimal","is proposed.The limit of some functions can be quickly and accurately obtained by using this form,which provides an important method for solving some limit problems in postgraduate entrance examination and the college student mathematics competition.