Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

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).

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.

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

Terms you should be able to define: horizontal asymptote line, oblique (slant) asymptote, limit at infinity, approaching infinity (in terms of limits)

Mini-Lectures and Examples

Supplementary Resources (optional)

rev. 2020-10-10