An equivalent infinitesimal substitution problem of indeterminate limit from a literature and its correction
Journal: Region - Educational Research and Reviews DOI: 10.32629/rerr.v6i3.1829
Abstract
This article delves into the complexities of indeterminate limits and the pivotal role of infinitesimal substitution in their resolution. Within the realm of mathematical analysis, indeterminate limits--characterized by expressions such as "0/0" and "∞/∞"--pose a significant challenge to traditional limit computation techniques. Equivalent infinitesimal substitution is applied to reduce the difficulty of calculation in solving indeterminate limit problems. However, the substitution cannot be directly applied to indeterminate infinitesimal subtraction and addition. This paper points out the problem of equivalent infinitesimal substitution in the indeterminate limit calculation which includes addition and subtraction used in many papers, and amends the infinitesimal substitution theorem given in the papers.
Keywords
infinitesimal; equivalent infinitesimal substitution; indeterminate limit
Funding
The project is supported by the Sichuan Association for Non-Government Education with the project number MBXH23YB85 for the year 2023.
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[2] Jie DP. 2017. Research on the teaching extension of properties and applications of equivalent infinitesimal. Journal of Hefei Normal University, 35(3): 39-42.
[3] Xu QH, Wang RX, Zhao QB, et al. 2021. Reflections on the use of equivalent infinitesimal substitution in the calculation of limits involving addition and subtraction. Journal of Mathematical Learning and Research, 23: 128-129.
[4] Xiao ZT. 2021. Extension of equivalent infinitesimal substitution in limit operations. Research in Higher Mathematics, 24(5): 30-32.
[5] Huang YM, Na L. 2017. Teaching considerations for "equivalent infinitesimal substitution" in calculating limits. Journal of Southwest Normal University (Natural Science Edition), 42(7): 170-174.
[6] Wang XH. 2017. Research on the equivalent substitution of infinitesimal quantities in variable upper limit integral limit formulas. Journal of Jiamusi Vocational College, 2: 308-309.
[7] Xu ZJ. 2018. Some conclusions involving trigonometric and inverse trigonometric functions in the context of equivalent infinitesimal substitution. Journal of Mathematical Learning and Research, 11: 8-10.
[8] Zhang L. 2022. Application of equivalent infinitesimal in the limit of power functions with indeterminate forms. Research in Higher Mathematics, 25(05): 57-58.
[9] Department of Mathematics, Tongji University. 2014. Higher Mathematics Volume 1 (Seventh Edition). Beijing: Higher Education Press, 45-55.
[10] Han JX, Wang XQ. 2019. On the methods and issues to be aware of in solving limits. Research in Higher Mathematics, 22(5): 19-24.
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