Generalization about Conditions for Replacement of Equivalent Infinitesimal Variable When Limiting

Replacement of equivalent infinitesimal variable is an important and convenient method for limiting.However,there are rarely sufficient conditions about replacement of equivalent infinitesimal variable among addition and subtraction.In this article,we obtain a sufficient and necessary condition for replacement of equivalent infinitesimal variable among addition and subtraction.Meanwhile,we give a sufficient condition,which is very easy to judge in specific calculation.All these results broaden the condition for limiting by replacement of equivalent infinitesimal variable.