Question

急！英语高手进，帮忙翻译一下

摘 要:拉格朗日（Lagrange）中值定理是重要的微分中值定理之一。本文简要叙述了定理的内容，并且给出了定理的两种证明方法，例举了拉格朗日中值定理在数学中的主要应用，包括证明不等式，恒等式，求极限，判断单调性，根的存在性等。对拉格朗日中值定理的一些错误用法进行简要分析。最后对定理条件进行弱化，进行推广得到更一般的形式。
关键字：拉格朗日中值定理；极限；不等式；根的存在性；推广

以上部分帮忙翻译一下 非常感谢 分比较少不好意思 下次补上 谢谢了

Answer 1

Abstract: Lagrange (Lagrange) value theorem is an important one of the Mean Value Theorem. This paper describes the content of the theorem, and theorems are given two proofs, cite the Lagrange mean value theorem in the mathematics major applications, including that inequality, identity, Limit, determine monotonicity, root The existence of such. Lagrange mean value theorem on the wrong usage of some brief analysis. Finally, Theorem weakened condition, to promote more general form.
Keywords: Lagrange mean value theorem; limit; inequality; root existence; Promotion