极限和无穷小分析

摘要

摘要：极限是微积分中非常重要的基础知识，极限的定义是一个朴素的逻辑命题，其中涉及到存在性，任意性和不等式的问题. 本文探讨了极限的基础概念及其在现代科学计算中的关键作用.我们以极限、无穷小为重点，深入探讨了它们在定义连续性、导数和数值表示技术方面的意义.我们将无穷小与科学计数法相提并论，阐明它们在促进复杂计算和模拟现象中的应用.通过分析，我们展示了极限和无穷小如何为理解函数行为、解释函数和极限计算提供了一个强大的框架.

Abstract: Limit is a very important basic knowledge in calculus. The definition of limit is a simple logical proposition, which involves the problems of existence, arbitrariness and inequality. This paper discusses the basic concept of limit and its key role in modern scientific computation. We focus on limits and infinitesimals and explore in depth their significance in defining continuity, derivatives and numerical representation techniques. We draw parallels between infinitesimal and scientific numeration to illustrate their use in facilitating complex calculations and simulating phenomena. Through our analysis, we show how limits and infinitesimals provide a powerful framework for understanding function behavior, interpreting functions, and limit computation.