等价无穷小代换定理的拓展

On the Generalization of Equivalence Infinitesimal Replacement Theorem

利用等价无穷小代换求极限可以简化计算,基于此,本文主要探讨了极限式中含加减因子及幂指结构时用等价无穷小代换求极限的问题,对教材中未提及的极限式中含加减关系、复合结构及幂指结构的情况加以补充,并给出了相应代换的条件和应用实例。

The calculation for finding limits can be simplified with equivalence infinitesimal replacement theorem. This paper mainly discusses how to use the equivalence infinitesimal replacement theorem fred limits for the limiting equations with plus -minus factor, complex structure and power exponent structure; at the same time, the ones which have not mentioned in teaching materials are put forward, and some relevant replacement conditions and application examples are given.