Question

高手，你还能再帮我翻译一下，我只有来求助你了。真的翻译不了。急！！！

海涅定理是数学分析课程中重要的定理之一，它是沟通函数极限与数列极限之间的桥梁，它的应用贯穿在数学分析课程乃至高等数学等多门课程之中. 数学分析教材在讨论海涅定理时都只就 一种情形来讨论，本文将补给并证明其他五种情形函数极限的海涅定理，同时对海涅定理的应用作一些探讨、总结.

Answer 1

Heine theorem is one of the important theorems in mathematical analysis courses. It builds a bridge between function limits and series limits, and its applications emerge through many courses in mathematical analysis or even advanced mathematics. Usually, mathematical analysis textbooks only discuss one general case about Heine theorem, while this paper supplements and proves Heine theorem in the other five cases of function limits, and explores and summarizes the applications of Heine theorem.