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In this paper we propose a method for proving some exponential inequalitiesbased on power series expansion and analysis of derivations of thecorresponding functions. Our approach provides a simple proof and generates anew class of appropriate inequalities, as well as allows direct establishmentof the dependence between (the exponent of) some functions that occur as boundsof the approximation and the interval in which the corresponding inequalityholds true.

One method for proving some classes of exponential analytic inequalities