LIMITS

Authors

  • Yuldoshev Jonibek Azamqulovich head teacher of mathematics at the Academic Lyceum of the Turin Polytechnic University in Tashkent Author

Keywords:

limits, calculus, epsilon-delta definition, continuity, convergence, derivatives, integrals

Abstract

Limits in mathematics underpin calculus by rigorously defining how functions and sequences approach specific values, enabling analysis of continuity, derivatives, and integrals. This article explores their historical development, formal definitions, diverse types, key theorems, extensions to modern analysis, and broad scientific applications, emphasizing their role as a cornerstone for understanding dynamic processes across disciplines.

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References

1. Limitlarning asosiy xossalari, aniqmasliklar va ularni ochish [Basic properties of limits, indeterminacies, and their resolution]. (n.d.). TIIAME University Repository. Retrieved January 8, 2026, from ttps://staff.tiiame.uz/storage/users/693/presentations/VWzvbhz7q0eEn0RaXjZgd41WVnxdonpPojzSSC7q.pdf

2. Xushvaqov, M. (n.d.). Matematik analiz [Mathematical analysis]. Ziyouz Library. Retrieved January 8, 2026, from https://www.ziyouz.com/books/kollej_va_otm_darsliklari/matematika/Matematik%20analiz%20(M.Xushvaqtov).pdf[2]

3. Ibragimov, N. Sh. (2022). Limit tushunchasining paydo bo‘lishi, ajoyib limitlar [Origin of the limit concept, remarkable limits]. Zenodo. https://doi.org/10.5281/zenodo.6758612

4. Limitlar nazariyasi (Shtols teoremasi) [Theory of limits (Stolz theorem)]. (2025). Scribd Academic Document. Retrieved January 8, 2026, from https://www.scribd.com/document/738128359/LIMITLAR-NAZARIYASI-Shtols-teoremasi-oxirgi-variant

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Published

2026-01-22