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Dobbs, David E. – International Journal of Mathematical Education in Science and Technology, 2011
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…
Descriptors: Geometric Concepts, Calculus, Mathematics, Mathematics Education
Dobbs, David E. – International Journal of Mathematical Education in Science and Technology, 2010
This note develops and implements the theory of polynomial asymptotes to (graphs of) rational functions, as a generalization of the classical topics of horizontal asymptotes and oblique/slant asymptotes. Applications are given to hyperbolic asymptotes. Prerequisites include the division algorithm for polynomials with coefficients in the field of…
Descriptors: Calculus, Mathematics Instruction, Algebra, Mathematical Concepts