Limits at Infinity and Asymptotes: Read the Ends and Blow-Ups

This English Calculus I lesson explains how to read rational-function behavior at infinity and near vertical asymptotes. It defines limits at infinity and infinite limits, distinguishes horizontal, vertical, and oblique asymptotes, and shows why a removable hole is not a vertical asymptote. The sequence follows the standard treatment of limits at infinity and asymptotes in OpenStax Calculus Volume 1, Section 4.6. 1

You will work three complete examples: a same-degree rational function, one-sided signs at a vertical asymptote, and polynomial division for an oblique asymptote. The closing workflow separates domain restrictions, cancellation, one-sided limits, end limits, and the final asymptote statement.