等价无穷小的性质及其运用推广

Expand and Application of Equivalent Infinitesimal's Character

等价无穷小在求极限的运算中和在正项级数的敛散性判断中有着重要的作用,能达到洛必达法则所不能取代的作用,通过举例对比了不同情况下等价无穷小的应用,以及在应用中应注意的条件。正确利用等价无穷小,可使一些原本复杂的问题变得简单,同时避免出错。

Equivalent Infinitesimal plays important role in both operation of test for Limit and determine whether the positive series converges or diverges. Rod can reach the law that can not be replaced by L＇ Hospital Rule. This paper compares the application of equivalent Infinitesimal in different conditions, to pay attention to the condition in application of Equivalent Limit. To use the equivalent infinitesimal correctly, some complicated questions can become simple, at the same time to avoid making mistakes.