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Volume 4,Issue 3

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26 February 2026

Research on A Class of Infinite Radical Nested Limit Problems Based on MATLAB

Peiying Wang1 Zhenhao Zhang1 Weikuo Huang1 Yanzhang Li1 Xuyang Chen1
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1 College of General Education, Guangzhou Institute of Science and Technology, Guangzhou 510540, Guangdong, China
EIR 2026 , 4(2), 115–123; https://doi.org/10.18063/EIR.v4i2.1552
© 2026 by the Author. Licensee Whioce Publishing, Singapore. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License ( https://creativecommons.org/licenses/by/4.0/ )
Abstract

In this paper, we use the cosine function to calculate the limit of an infinite root nested, modify the constants in the topic, and use the same method to calculate the limit. We extend the topic to the general case, and derive a limit formula containing the anti cosine function. Then we use the analogical reasoning method to derive a limit formula containing the anti hyperbolic cosine function. The curve of the function is drawn with mobile MATLAB, and the correctness of the results is verified, it shows the powerful function of MATLAB.

Keywords
infinite radical nesting
analogical reasoning
visualization
MATLAB; limit
Funding
School-level Research Project of Guangzhou Institute of Science and Technology: First-class Offline Course of Advanced Mathematics (Project No.: 2022TYK07)
References

[1] Dong Y, Wang JL, Jin M Z, 2016, Review Guide to Calculus (2nd ed.). Shandong University Press, 1-13.
[2] Zhou QY, Ma CX, Luo H, et al., 2016, Visual Advanced Mathematics with MATLAB (Volume I). Hunan University Press, 1-54.
[3] Wang PY, Lu HY, Xu QH, et al., 2020, Multiple Solutions and Visualization of a Postgraduate Entrance Examination Question. Journal of Hengyang Normal University, 41(6): 24-28.
[4] Wang PY, Xu YC, Chao JH, et al., 2019, Limits and Visualization of Recursive Sequences of Arithmetic, Geometric and Harmonic Means of Multiple Positive Numbers. Journal of Hengyang Normal University, 40(3): 6-9.
[5] Xu QH, Chao JH, Xu YC, et al., 2019, Limit and Visualization of Recursive Sequence of Geometric Mean. Mathematics Learning and Research, (7): 2-5.
[6] Wang PY, Zhuo HS, Huang SM, 2021, Continuity Calculation and Visualization of Partial Derivatives of Binary Functions. Journal of Hengyang Normal University, 42(3): 29-32.
[7] Wang PY, Zhang T, Zhang X, et al., 2021, Exploration on the Angle Problem of Three Intersecting Lines in a Square. Journal of Hengyang Normal University, 42(6): 70-74.

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