中文摘要：

拉格朗日（Lagrange）中值定理是微分中值定理的核心定理之一，本文主要通过例题来说明如何使用La-grange中值定理来证明恒等式、不等式、方程根的存在性、极限以及级数的收敛性的方法。

英文摘要：

Lagrange＇s mean value theorem is one of the core theo-rems in differential mean value theorems. This article explains how to use the Lagrange＇s mean value theorem to prove identity, inequality, the existence of root of equation, limit as well as the convergence of the series by way of examples.