Question

英语翻译，，帮忙修改一下

摘要：在高等数学的学习中，我们经常可以看到中值定理在数学中的频繁使用，其定理的内容也很容易理解，但在具体的解题过程中往往存在很多的偏差性，使得在解题过程中存在很多的无用步骤出现。故而如何能够合理巧妙的在解题中使用到中值定理的相关内容至关重要。只有进行合理的总结相关规律，那么解题的步骤和难度才会降低很多，在何时使用中值定理，使用哪个中值定理，使用何种相关定理成为了最关注的焦点问题。因此本文根据经验做出相关总结，讲述的中值定理主要有三方面，包括罗尔中值定理、拉格朗日中值定理、柯西中值定理。通过实际问题的提出，详细讲解中值定理的具体求解方法和定理相关使用技巧。

关键字：罗尔中值定理; 拉格朗日中值定理; 柯西中值定理;

The use of mean value theorem
Abstract：In higher mathematics learning, we often can see the frequent useof mean value theorem in mathematics, the theorem of content is also very easyto understand, but in concrete tend to have a lot of deviation in the processof problem solving, that exist in the process of problem solving a lot ofuseless steps. So how to reasonably clever use to the mean value theorem in theproblem solving related content is very important. Only reasonable summary ofthe related laws, then the problem solving steps and the difficulty will reducea lot of, when using the mean value theorem, which mean value theorem, whichbecame the focus of the most relevant theorem. So this article according to relevantexperience summary, there are three main aspects of the mean value theoremabout, including differential mean value theorem, Lagrange theorem and cauchymid-value theorem are obtained. Through the practical problems, is proposed inthis paper explains the concrete solving method of mean value theorem andtheorem related to use skills.

Keyword：Differential mean value theorem； Lagrange mean valuetheorem； Cauchy mean valuetheorem

Answer 1

The use of mean value theorem
Abstract：In higher mathematics learning, we often can see the frequent use of mean value theorem in mathematics, the theorem of content is also very easy to understand, but in concrete tend to have a lot of deviation in the process of problem solving, that exist in the process of problem solving a lot ofuseless steps. So how to reasonably clever use to the mean value theorem in theproblem solving related content is very important. Only reasonable summary ofthe related laws, then the problem solving steps and the difficulty will reducea lot of, when using the mean value theorem, which mean value theorem, whichbecame the focus of the most relevant theorem. So this article according to relevantexperience summary, there are three main aspects of the mean value theoremabout, including differential mean value theorem, Lagrange theorem and cauchymid-value theorem are obtained. Through the practical problems, is proposed inthis paper explains the concrete solving method of mean value theorem andtheorem related to use skills.

Keyword：Differential mean value theorem； Lagrange mean valuetheorem； Cauchy mean valuetheorem