高等数学中隐秘单侧极限的求法研究

Methods for Computing Hidden One-Sided Limits in Advanced Mathematics

摘要: 单侧极限是学生学习极限概念时的一个难点。本文通过具体题目分析高等数学中最常见的隐秘单侧极限(以$e^{\infty }$ 型极限为代表)出现的一些问题，给出相应的处理方法，并对解题思想进行归纳总结，进而加以推广。

Abstract: One-sided limits are often a difficult topic for students when they first learn the concept of limits. This paper analyzes some typical problems involving the most common hidden one-sided limits in advanced calculus, with $e^{\infty }$ -type limits as a representative example. For these problems, we propose corresponding solution methods, summarize the underlying problem-solving ideas into a unified framework, and further show how this framework can be extended and applied to related situations.