Fungsi kontinu

Definisi, teorema, dan aplikasinya dalam berbagai disiplin ilmu

Abstract

Continuous functions are one of the fundamental concepts in mathematical analysis with broad applications across various disciplines. This paper discusses the definition of continuous functions both formally and intuitively, as well as key theorems underlying them, such as the Bolzano Theorem and the Limit Theorem. An explanation of the criteria for continuous functions, particularly in the context of the epsilon-delta definition, is also provided to give a deeper understanding of their properties. Furthermore, this paper explores the applications of continuous functions in various fields, including calculus, physics, economics, and engineering, and how this concept is used to solve practical problems such as load distribution in structural design and cost optimization in production. For example, continuous functions are used to design stable and efficient bridges and in economic models to minimize costs and maximize profits. Further research on continuous functions holds the potential to make significant contributions to developing solutions for more complex scientific and technical challenges in the future. The paper concludes with suggestions for improving mathematics education and fostering multidisciplinary collaboration in applying the concept of continuous functions across various sectors..