利用洛必达法则求解函数极限及其在物理学与经济学中的应用分析  

Applying L’Hospital’s Rule to Evaluate the Limit of a Function and Its Practical Applications in Physics and Economics

作　　者：于宾若 

机构地区：[1]辽宁师范大学数学学院,辽宁 大连

出　　处：《应用数学进展》2024年第8期3625-3631,共7页Advances in Applied Mathematics

摘　　要：函数在数学和科技发展中具有重要作用,求解函数极限的方法在函数研究中占据重要地位。极限是高等数学的基础,极限问题是研究的核心和难点。现有文献中极限求解方法的研究多集中于理论阐述,缺乏实际应用案例的分析。本文在系统介绍极限求解方法的基础上,结合经济学、物理学等实际应用案例,旨在弥补这一不足。本文探讨了利用洛必达法则求解函数极限的方法,并分析了其在物理学与经济学中的实际应用。首先,概述了洛必达法则的理论基础及其在处理不定式极限问题中的优势。然后,通过具体实例,详细讲解了如何应用洛必达法则解决物理学中的速度和加速度计算问题,以及经济学中的边际成本和边际收益计算问题。通过这些实例,展示了洛必达法则在不同领域的广泛应用和重要性。本文旨在为读者提供一个全面而实用的参考,使其在实际问题中能够有效应用洛必达法则进行函数极限的求解。The function plays a crucial role in the development of mathematics, science, and technology. The method of solving the limit of a function is essential for studying functions. Limit serves as the foundation of higher mathematics, and addressing limit problems represents the core challenge in research. Existing literature primarily focuses on theoretical elaboration when it comes to methods for solving limits, lacking analysis of practical application cases. This paper aims to address this gap by systematically introducing limit solution methods and combining them with practical application cases from economics and physics. The paper discusses the use of L’Hospital’s rule in solving function limits and analyzes its practical applications in physics and economics. It first summarizes the theoretical basis of L’Hospital’s rule and its advantages in dealing with infinite limit problems. Subsequently, it explains how to apply L’Hospital’s rule to calculate velocity and acceleration in physics, as well as marginal cost and benefit in economics. These examples demonstrate the wide-ranging applications and significance of L’Hospital’s rule across different fields. The purpose is to provide readers with a comprehensive reference that enables effective application of L’Hospital’s rule to solve functional limits within practical problems.

关 键 词：洛必达法则 极限理论应用 计算方法 

分 类 号：G63[文化科学—教育学]