Application of Taylor's Mean Value Theorem
and Formula

Su Xiao-ya; Zhai Yan-hui

doi:https://doi.org/10.14445/22315373/IJMTT-V66I9P513

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 9 | Year 2020 | Article Id. IJMTT-V66I9P513 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I9P513

Application of Taylor's Mean Value Theorem and Formula

Su Xiao-ya, Zhai Yan-hui

Citation :

Su Xiao-ya, Zhai Yan-hui, "Application of Taylor's Mean Value Theorem and Formula," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 9, pp. 105-116, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I9P513

Abstract

This paper mainly investigated the application of Taylor's mean value theorem and formula. The beginning of this article introduces the related concepts of mean value theorem and Taylor formula and its proof, then there is the key part, we mainly introduced the nine applications, presented in the form of examples. Then the Taylor mean value theorem and its formula in the limit of function, proving equality and inequality, discriminating convergence of series and generalized integral, estimating the boundary of derivative function and in the application of function equation are summarized.

Keywords

Taylor’s formula, Taylor mean value theorem, the limit, inequality.

References

[1] Liu Yulian et al.Handout on Mathematical Analysis (volume I)[M]. Beijing.Higher Education Press.2008:264-277
[2] Pei Liwen.Typical problems and methods in mathematical analysis [M]. Higher Education Press.1993:241-254
[3] Ferdinand.Application and techniques of Taylor's formula [J]. Journal of west anhui university.2001,19(3)
[4] Yan Yongxian.Taylor's mean value theorem in inequality proof [J]. Journal of zhejiang university of science and technology.2010,22(3)
[5] Gong Dongshan et al.Taylor's mean value theorem in a class of limit calculations [J]. Journal of chaohu university.2008,10(6)
[6] Wang Sanbao.An example of Taylor's formula [J]. Journal of higher correspondence. 2005,19 (3)