An Analytical Exploration of Limits and Infinitesimals

Abstract

Limits and infinitesimals are crucial components of calculus and advanced mathematics. This paper discusses the fundamental concepts and applications of limits, focusing on their significance in defining continuity, derivatives, and numerical representation techniques. We draw a parallel between infinitesimals and scientific notation to illustrate their role in facilitating complex calculations and simulating phenomena. Through analysis, we demonstrate how limits and infinitesimals provide a robust framework for understanding function behavior, explaining functions, and calculating limits.