柯西中值定理的两种新证法  

Two New Proofs of Cauchy Mean Value Theorem

作　　者：牛丽娜 古丽米热·尔肯 热比古丽·吐尼亚孜 NIU Lina;GULMIRE Arkin;RABIGUL Tuniyaz(Xinjiang Institute of Technology,Akesu 843100,China)

机构地区：[1]新疆理工学院,新疆阿克苏843100

出　　处：《广东农工商职业技术学院学报》2022年第2期49-50,59,共3页Journal of Guangdong Agriculture Industry Business Polytechnic

基　　金：国家自然科学基金资助项目(11861061)。

摘　　要：设函数f(x)和g(x)在[a,b]上连续,在(a,b)内可导.直接从拉格朗日中值定理出发,证明了至少存在一点ξ∈(a,b),使得(f(b)-f(a))g'(ξ)=(g(b)-g(a))f'(ξ).此外,从以P=(f(a),f(b)),Q=(g(a),g(b))为端点的两个向量是否平行的判别式(二阶行列式)出发,证明了同样的结论.Suppose that two functions f(x)and g(x)are continuous over[a,b]and have derivative in(a,b).By means of Lagrange theorem directly,it shows hat there exists aξ∈(a,b)such that(f(b)-f(a))g'(ξ)=(g(b)-g(a))f'(ξ).Moreover,By means of the determinant that checks whether the two vectors represented by P=(f(a)-f(b))and Q=(g(a)-g(b))are parallel,the same result is proved.

关 键 词：连续 可导 罗尔定理 拉格朗日定理 

分 类 号：O13[理学—数学]