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2005•Journal of Zhuzhou Teachers CollegeRequires access

Unified Demonstration and Generalization of Intermediate Value Formula in Infinitesimal Calculus

Runhui Liu

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Abstract

Cauchy Intermediate Value Formula has unified the diversified intermediate value formulas in infinitesimal and has established the internal relations between integral intermediate value formulas and differential ones. With Rolle Intermediate Value Formula and different assisting functions,some other intermediate value formulas can be demonstrated to be some diversified forms of Cauchy Intermediate Value Formula.Some generalized forms of infinitesimal intermediate value formula can be induced from Taylor Formula.

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Cauchy Intermediate Value Formula has unified the diversified intermediate value formulas in infinitesimal and has established the internal relations between integral intermediate value formulas and differential ones. With Rolle Intermediate Value Formula and different assisting functions,some other intermediate value formulas can be demonstrated to be some diversified forms of Cauchy Intermediate Value Formula.Some generalized forms of infinitesimal intermediate value formula can be induced from Taylor Formula.

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Available abstract

Cauchy Intermediate Value Formula has unified the diversified intermediate value formulas in infinitesimal and has established the internal relations between integral intermediate value formulas and differential ones. With Rolle Intermediate Value Formula and different assisting functions,some other intermediate value formulas can be demonstrated to be some diversified forms of Cauchy Intermediate Value Formula.Some generalized forms of infinitesimal intermediate value formula can be induced from Taylor Formula.

Key concepts: Infinitesimal, Mathematics, Value (mathematics), Generalization, Cauchy distribution, Differential (mechanical device), Differential calculus, Initial value problem

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