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Course: Calculus I
Topic: Limits and Continuity
Subtopic: Limits at Infinity

Overview

A limit at infinity means a limit whose x-value is approaching positive or negative infinity. Graphically these limits explore the function as x grows infinitely large or infinitely small. If the limit exists it shows the function has a horizontal asymptote line at that limiting value. Limits at infinity can also be used to find an oblique asymptote line (or asymptote curve).

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 1.8.1 Understand that limits at infinity can provide information about the graph of the function as it approaches a horizontal or oblique asymptote line
• 1.8.2 Algebraically evaluate limits whose x-value is approaching positive or negative infinity
• 1.8.3 Use algebraic methods to simplify a rational function so that a limit at infinity can be determined

Terminology

Define: horizontal asymptote line, oblique (slant) asymptote, limit at infinity, approaching infinity (in terms of limits)

Text Notes

When evaluating a limit at infinity a trick that is sometimes useful is to force the variable into denominators of fractions that would then be made negligible (thus approach zero) as the variable approaches infinity. An example will be presented in class.

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