关于幂指函数极限计算中等价代换问题的研究

The Studies on the Equivalent Substitution in Limit Calculation of Power—Exponential Fuctions

一般在微积分教程中,可应用给出的等价代换的定理去求解两个函数比或两个函数乘积的极限;但对于求幂指函数极限,可重使用等价代换定理,微积分学教程中却没有论及。本文对此问题进行论证,指出在幂指函数极限计算中,可以使用等价无穷小或等价无穷大代换。代换后的极限形式变得简单易解。

Generally,the equivalent substitution theorem has been given out in the couse of differential and integral calculus.It can be used to calculate the limit of ratio or prod- uct of two fuctions.In calculus,it has not been proved whether or not the equivalent substitution theorem can be applied to the limit calculation of power-exp ential fac- tions.This paper discussed the problem and pointed out that the limit of power-expo- nential fuction can be calculated by the substitution of equivalent infinitely great or in- finitely small.The substitution made the limit calculation form more sample and more easily be understood.