关于微积分课程中的两个重要极限  

On Two Important Limits in Calculus

作　　者：杨森 YANG Sen(School of Artificial Intelligence,Anshan Normal University,Anshan Liaoning 114007,China)

机构地区：[1]鞍山师范学院人工智能学院,辽宁鞍山114007

出　　处：《鞍山师范学院学报》2025年第2期1-6,共6页Journal of Anshan Normal University

基　　金：鞍山师范学院科研项目(23KYXM032).

摘　　要：微积分课程中的两个重要极限分别与三角函数和指数函数有关.通过分析余弦函数与正弦函数性质的推演关系,证明正弦函数是满足第一个重要极限式的唯一函数;通过分析指数函数性质的推演关系,证明指数函数是满足第二个重要极限式的唯一函数.In calculus,two important limits are associated with trigonometric and exponential functions.By analyzing the properties and relationships of cosine functions and sine functions,it is shown that the exponential function and the trigonometric function are the only functions that satisfy these two important limit expressions.By analyzing the deduction relationship of the properties of exponential functions,it is proved that the exponential function is the only function that satisfies the second important limit formula.

关 键 词：两个重要极限 指数函数 余弦函数 正弦函数 

分 类 号：O151.2[理学—数学]