在高等数学教学中关于无穷小量比较和性质的处理

Processing of the Comparison and Nature of Infinitesimal Order in Higher Mathematics Teaching

在《高等数学》教材中，一般只介绍了关于无穷小量比较的几个概念，如高阶无穷小、低阶无穷小、同阶无穷小、阶无穷小、等价无穷小，以及利用等价无穷小求极限的替换定理，但对于无穷小比较中的概念的理解、等价无穷小的性质基本没有介绍，使学生在理解概念及应用性质时出现偏差。

＂Higher Mathematics＂ textbook introduces several concept about the comparison of infinitesimal order, such as infinitesimal of higher order, infinitesimal of lower order, infinitesimal of the same order, infinitesimal of the k order, the equivalent infinitesimal, as well as the replacement theorem which use the equivalent infinitesimal to get limit, but for the understanding of the concept of the comparison of infinitesimal order, basically no introduction of the equivalent infinitesimal nature, to enable students to go awry in understanding the concept and the nature of application.