一道极限题的逐步延伸分析

A Step-by-step Extension of a Limit Question

文中首先讨论了极限lim_(x→0)(1/x^(n)-1/sin^(n)x)n∈N的情况,然后讨论极限lim_(x→0^(+))(1/x^(α)-1/sin^(α)x)(α>0)的情况,最后讨论了当f(x)~x(x→0)时lim_(x→0)(1/x-1/f(x))及lim_(x→0^(+))(1/x^(α)-1/f^(α)(x))(α>0)的情况.

In this paper,we discuss,respectively,the limit lim_(x→0)(1/x^(n)-1/sin^(n)x)n∈N,lim_(x→0^(+))(1/x^(α)-1/sin^(α)x)(α>0),lim_(x→0)(1/x-1/f(x)),and lim_(x→0^(+))(1/x^(α)-1/f^(α)(x))(α>0) when f(x)~x(x→0).