The Importance of the Concepts of Limit and Continuity in Mathematical Analysis

Abstract

This article examines the concepts of limit and continuity, which are fundamental concepts in mathematical analysis, and explains their theoretical and practical significance. The concept of a limit is used to study the behavior of a function at a specific point and its infinitesimal changes. Continuity, on the other hand, describes the uninterrupted behavior of a function. The article also provides a detailed discussion of the role of these concepts in derivatives, integrals, differential equations, and the solution of practical mathematical problems.