关于分式未定式极限的多解模式研究

Study on the Multiple Solution Model of the Limit of Fractional Indefinite

摘要: 高等数学以极限思想为基础，极限又以未定型极限的求解最难。求未定式的极限是高等数学中常见的题型，而洛必达法则是众多方法中最行之有效的方法。但是洛必达法则不仅仅是唯一的求解方式，洛必达法则常常与等价无穷小替换，四则运算法则，约去非零因子法，泰勒公式展开等方法结合使用，并且洛必达法则的使用也有一些限制条件。本文针对分式未定式求极限的多解模式进行研究，特别针对未定式型中或者等分式未定式的求解给出了多种方式进行解答，讨论了分式未定式极限的基本求解方法，并引入了泰勒n级无穷小等价替换对其难点进行了分析，力求将培养学生能力与课程教学紧密结合。

Abstract: Higher mathematics is based on the idea of limit, and it is the most difficult to solve the undefined limit. Finding the limit of the undefined form is a common question type in higher mathematics, and Lobita’s rule is the most effective method among many methods. However, Lopida’s rule is not the only solution. Lopida’s rule is often used in combination with equivalent infinitesimal, equivalent infinity, four algorithms, reduce non-zero factors, Taylor expansion and other methods, and there are some restrictions on the use of Lopida’s rule. In this paper, we study the multiple solution mode of finding the limit of the fractional infinitive. Especially for undefined type or . The solution of the fraction infinitive gives a variety of ways to solve, the difficulties are analyzed by in-troducing Taylor’s n-order infinitesimal equivalent substitution and strives to closely combine the training of students’ ability with the course teaching.