对两道未定式解法的分析与探讨

On the Solutions of Two Indeterminate Forms

以一道未定式的求解为例,通过对使用洛必达法则求解时求导过程比较复杂的原因分析,提出在求导前对函数进行预处理的思想,并指出等价无穷小替换是有效的处理方法.而针对另一道未定式问题,指出相关文献为论证一种错误的解法而使用的反例是错的,给出该解法存在错误的具体说明.

Existing methods for solving limits of indeterminate forms are relatively complicated.An idea which prearranges functions before using L＇Hospital＇s Rule is proposed.It is shown that the equivalent infinitesimal replacement can be effective.By exploring a limit problem of another indeterminate form,the mistake of a counter-example,used by related articles in order to show the error of a solution,is revealed.The detail explanation about this mistake is provided.