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2020•Journal of Physics Conference SeriesOpen access

Discussion on the application of Lagrange mean value theorem

Yinshan Jiang

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Abstract

Abstract The Lagrange mean value theorem has been widely used in the following aspects; ( 1 )Prove equation; ( 2 )Proof inequality; ( 3 ) Study the properties of derivatives and functions; (4) Prove the conclusion of the mean value theorem; (5) Determine the existence and uniqueness of the roots of the equation; (6 ) Use the mean value theorem to find the limit.

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Abstract The Lagrange mean value theorem has been widely used in the following aspects; ( 1 )Prove equation; ( 2 )Proof inequality; ( 3 ) Study the properties of derivatives and functions; (4) Prove the conclusion of the mean value theorem; (5) Determine the existence and uniqueness of the roots of the equation; (6 ) Use the mean value theorem to find the limit.

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Available abstract

Abstract The Lagrange mean value theorem has been widely used in the following aspects; ( 1 )Prove equation; ( 2 )Proof inequality; ( 3 ) Study the properties of derivatives and functions; (4) Prove the conclusion of the mean value theorem; (5) Determine the existence and uniqueness of the roots of the equation; (6 ) Use the mean value theorem to find the limit.

Key concepts: Mean value theorem (divided differences), Mathematics, Picard–Lindelöf theorem, Limit (mathematics), Uniqueness theorem for Poisson's equation, Uniqueness, Value (mathematics), Mean value

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