journal6 ›› 2006, Vol. 27 ›› Issue (3): 8-11.

• Mathematics • Previous Articles     Next Articles

Asymptoticity of the Intermediate Point in the Mean Value Theorem of Integrals


  1. (Zhangjiajie College,Jishou University,Zhangjiajie 427000,Hunan China)
  • Online:2006-05-25 Published:2012-09-11

Abstract: Suppose function f(t) be continuous in [a,x],and n the order differentiable at point a,and f(n)(a)≠0 then ξx in mean value theorem of integration satisfies lim x→a {f′(a)[(ξx-a)/((x-a)n)-1/2·1/((x-a)n-1)]+(f″(a))/(2!)[((ξx-a)2/((x-a)n)-1/3·1/((x-a)n-2)]+…+(f(n)(a))/(n!)[((ξx-a)n)/((x-a)n)-1/(n+1)]}=0.

Key words: mean value theorem of integrals, intermediate point, asymptoticity

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