A General Formula for Asymptotes of Rational Polynomial Functions

TL;DR

This paper introduces a novel formula for calculating asymptotes of rational polynomial functions using matrix determinants, offering an alternative to traditional methods like Euclidean division and limit evaluation.

Contribution

The paper presents a general determinant-based formula for asymptotes of any rational polynomial function, expanding computational tools beyond standard techniques.

Findings

The formula applies to all degrees of rational polynomial functions.

It simplifies the process of finding asymptotes through matrix determinants.

Provides a new computational approach complementing existing methods.

Abstract

We propose a formula for finding the horizontal, oblique or curvilinear asymptote of any rational polynomial function of any positive degree, as a sum of matrix determinants formed directly from the coefficients of the terms in the given polynomial. This formula provides a new means of computing asymptotes in addition to the standard methods of Euclidean division and the evaluation of limits.