APPLYING INFINITESIMAL EQUIVALENCE IN CALCULATION OF FUNCTION LIMITS

Abstract

Many problems of analytical mathematics lead to calculation of limits of a function. Therefore, the calculation of limits of a function has attracted much attention of mathematicians. Only when it is in anamorphous form does the calculation of the limits of a function appear really difficult to be solved. Among amorphous forms, the 0/0 amorphous one is the most common and important, for most of other amorphous forms can be converted into 0/0. The nature of the 0/0 amorphous form is comparison between two infinitesimal quantities.In this article, we have chosen the exponential function as an intermediary infinitesimal quantity, whereby instead of comparing two infinitesimals together, we are to compare them with the above infinitesimal intermediary. Thus, we move from the problem of comparing two infinitesimals to the one of comparing two exponential functions, which already has its own solution; therefore, we can obtain the results of the initial problem.