等价无穷小替换求极限的一些问题研究

Study on Limit Computation by Using the Replacement with Equivalent Infinitesimals

在利用等价无穷小替换求极限的过程中,有些分式的极限不能直接用等价无穷小替换.在讲授时,应该在掌握基本概念和基本原理的基础上,通过实际算例进行重点阐明和运用.针对不同的情形,给出了一些方法和建议.

During the limit computation, the replacement with equivalent infinitesimals is not applied di- rectly in some fractions. When teaching, some examples should be given to explain how to use them after the students have mastered the basic concepts and the basic principles. Some methods and advice are pro- posed for different cases.