Evaluation of limits including integrals by L’ Hôpital’s rule

Xinyao Xu

doi:10.54254/2753-8818/10/20230323

Research Article

Open access

Published on 17 November 2023

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Xu,X. (2023). Evaluation of limits including integrals by L’ Hôpital’s rule. Theoretical and Natural Science,10,96-100.

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Evaluation of limits including integrals by L’ Hôpital’s rule

Xinyao Xu *^,1,

¹ Shanghai Pinghe School

* Author to whom correspondence should be addressed.

https://doi.org/10.54254/2753-8818/10/20230323

Abstract

Limit is significant concept in mathematic analysis. Technically, limit’s definition in mathematics is that a variable in a function gradually approximates to a certain value in the changing process which cannot be ended. L’ Hôpital’s rule and Taylor expansion, together with other methods such as Stolz theorem, are usually used in measuring a limit’s value. In this paper, it will focus on some representative limits that are related to definite integrals. L’ Hôpital’s rule and Taylor's expansion are also jointed used so as to solve the problems. The main part of this work talks about the limit of the integration of trigonometric function, under which situation Taylor’s expansion is commonly utilized. This article talks about the polynomial’s integration as well, under which situation the approximation method is also employed. Trigonometric function and polynomial function are frequently appeared in evaluating limit. This means that this paper is summarizing the prime functions in integration-related limits.

Keywords

limit, L’ Hôpital’s rule, trigonometric function, Taylor expansion

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References

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Cite this article

Xu,X. (2023). Evaluation of limits including integrals by L’ Hôpital’s rule. Theoretical and Natural Science,10,96-100.

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About volume

Volume title: Proceedings of the 2023 International Conference on Mathematical Physics and Computational Simulation

Conference website: https://www.confmpcs.org/

ISBN：978-1-83558-131-5(Print) / 978-1-83558-132-2(Online)

Conference date: 12 August 2023

Editor：Roman Bauer

Series: Theoretical and Natural Science

Volume number: Vol.10

ISSN：2753-8818(Print) / 2753-8826(Online)

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