THEORETICAL AND PRACTICAL ASPECTS OF THE FIRST REMARKABLE LIMIT

Abstract

This paper investigates the theoretical and practical aspects of the first remarkable limit, which is one of the fundamental results of mathematical analysis. The first remarkable limit is proved using the fundamental theorem of differential calculus, namely Lagrange’s mean value theorem. This approach reveals the deep relationship between the concepts of limit and derivative. In addition, the role of the first remarkable limit in mathematical analysis is discussed, with particular emphasis on its significance in the theory of numerical series. The paper also demonstrates practical applications of this limit, including the mathematical pendulum model in physics and the analysis of electrocardiogram (ECG) signals representing cardiac activity in biology.