急啊!!哪位英语专业的同学帮我翻译一下论文的摘要？？

【Summary 】This text draw Luol, hit the intersection of value and theorem through the intersection of fee and the intersection of horse and theorem, construct, assist function to hit the intersection of value and theorem while being Lagrangian and then and Cauchy hit the intersection of value and theorem go on, prove. Utilize the value theorem (Luol's theorem, Lagrangian theorem, Cauchy's theorem) in the differential to solve some derivatives and terminal problems. Approach the function by multinomial, thus get formula of Taylor who wears inferior promise type residue and Lagrangian residue, utilize the launching type of McLaurin of the elementary function to solve the terminal and problem similar to evaluation. Through the study herein, demand to know the identification of value theorem and Taylor's formula in the differential skillfully, use the intersection of theorem and conclusion solve some correlated to it problem, make, can understand thinking of solving a problem of question this kind of clearly.
【Keyword 】Value theorem in the differential Taylor's formula Derivative Yu Xiang

【摘要】In this paper, leads to Fermat's theorem Rolle Mean Value Theorem, and then constructing auxiliary function of the Lagrange mean value theorem and Cauchy's Mean Value Theorem to prove that. The use of Differential Mean Value Theorem (Rolle theorem, Lagrange's theorem, Cauchy's theorem) to solve a number of derivative and limit the problem. Through the polynomial approximation to function, resulting in more than a Peano-type and Lagrange remainder of the Taylor formula, using elementary functions Maclaurin expansions to address the limits and the approximate evaluation of the problem. Through the study of this article requires proficiency in differential intermediate value theorem and Taylor's formula to prove, using theorem to solve a number of conclusions related questions, so can a clear understanding of this kind of problem solving ideas.
【关键词】Differential intermediate value theorem
Taylor formula
Derivative
More than

最后一个我不怎么会，所以。。。。别介意哦

This article draws out through the fima theorem rolls the theorem of mean, constructs the auxiliary function again the theorem of mean carries on the proof to west the Lagrange theorem of mean and the tan oak. (Rolls theorem using the differential theorem of mean, the Lagrange theorem, Cauchy's theorem) solves some derivatives and the limit question. Through multinomial approximating function, thus obtains has wears the Asian error term and Lagrange the error term Taylor formula, the use elementary function's Maclaurin expansion solves the limit and the approximate evaluation question. Through this article study, the request grasps the differential theorem of mean and the Taylor formula proof skilled, solves some using the theorem conclusion with it related question, enables to understand this kind of question explicitly the problem solving mentality.

Differential theorem of mean Taylor formula derivative error term

【摘要】In this paper, leads to Fermat's theorem Rolle Mean Value Theorem, and then constructing auxiliary function of the Lagrange mean value theorem and Cauchy's Mean Value Theorem to prove that. The use of Differential Mean Value Theorem (Rolle theorem, Lagrange's theorem, Cauchy's theorem) to solve a number of derivative and limit the problem. Through the polynomial approximation to function, resulting in more than a Peano-type and Lagrange remainder of the Taylor formula, using elementary functions Maclaurin expansions to address the limits and the approximate evaluation of the problem. Through the study of this article requires proficiency in differential intermediate value theorem and Taylor's formula to prove, using theorem to solve a number of conclusions related questions, so can a clear understanding of this kind of problem solving ideas. 【关键词】 Differential intermediate value theorem Taylor formula Derivative More than