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ALGEBRAIC APPROACH TO CALCULATIONS OF LIMITS IN HIGH SCHOOL

고등학교에서 극한값 계산의 대수적 접근

  • Received : 2025.04.15
  • Accepted : 2025.05.10
  • Published : 2025.05.31

Abstract

This study explores how the initial terms of the series expansions of exponential, logarithmic, and trigonometric functions can be derived using substitution and various algebraic techniques, without relying on differentiation. Based on these findings, the study discusses several educational implications, particularly in the context of high school mathematics instruction.

Keywords

References

  1. Ah Khloy A. (Retrieved May 3, 2025, from URL). limit x to 0 of (x-sinx)/x^3. (x-sinx)/x^3. https://www.youtube.com/watch?v=rQyVVUthpL8
  2. Han, I., & Kombarov A. (2004). The Role and Instruction of Geometry in Gifted Mathematics Education. Communications of mathematical education, 18(2), 265-276.
  3. Han, I. (2020). Learning Mathematical Expressions, Understanding Mathematics. Kyowoosa.
  4. Hwang, S., Kang, B., Yoon, G., Lee, G., Kim, S., Lee, M., Kim, W., Park, M., & Park, S. (2019). High School Calculus. MiraeN Publishing.
  5. Kim, S., Noh, J., Ma, M., Seo, B., Son, H., Shin, D., Shin, B., Lee, K., Lee, K., Lee, B., Lim, H., & Han, I. (2024). Introduction to Mathematics Education. Kyungmoonsa.
  6. Ko, S., Lee, J., Lee, S., Cha, S., Kim, E., & Cho, S. (2019). High School Calculus. Joeunchaek-Sinsago.
  7. Lyou, I., Han, I. (2011). A Study on Problem Solving Related with Geometric Interpretation of Algebraic Expressions. Communications of mathematical education, 25(2), 451-472. https://doi.org/10.7468/JKSMEE.2011.25.2.451
  8. Lyou, I. (2010). A Study on the Analysis and Application of Problem Information in the Process of Mathematical Problem Solving [Unpublished doctorial dissertation, Gyeongsang National University].
  9. Prime Newtons (Retrieved May 3, 2025, from URL). Limit (x-sin x)/x^3 as x goes to 0. https://www.youtube.com/watch?v=tvlBm BwmtE
  10. Mathematics Textbook Compilation Committee. (2005). College mathematics. Kyungmoonsa.
  11. Shin, H., Han, I., Choi, E., Lee, K., & Lew, M. (2001). Revisiting Korea's Seventh Mathematics Curriculum: Insights from International Educational Practices. Communications of Mathematical Education, 11, 291 – 296.