Abstract

This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and conics. Prerequisites include the division algorithm for polynomials with coefficients in the field of real numbers and elementary facts about limits from calculus. This note could be used as enrichment material in courses ranging from Calculus to Real Analysis to Abstract Algebra.

Citation

Dobbs, D.E. (2011). Polynomial Asymptotes of the Second Kind. International Journal of Mathematical Education in Science and Technology, 42(2), 276-282. Retrieved August 12, 2024 from https://www.learntechlib.org/p/167274/.

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Keywords

• Calculus
• Geometric Concepts
• mathematics
• mathematics education
• Validity