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S = contains supplemental resources
Course: Calculus I
Topic: Limits and Continuity
Subtopic: Infinite Limits

Overview

We have examined infinite limits (limits whose answer is infinity) graphically, but in this lesson we evaluate them algebraically. Limits that approach a real number but whose answer is positive infinity or negative infinity are graphically indicating a vertical asymptote exists at that real number.

CAUTION: Don’t confuse the following:

• Limits that do not exist such as at “jumps” or when the two side limits don’t match).
• Limits that technically do not exist because they are infinity. Recall limits technically must be real numbers. These can occur when the x is approaching a vertical asymptote line.
• Limits of functions as x approaches infinity (or negative infinity). These relate to horizontal asymptote lines or oblique (slant) asymptote lines.

Objectives

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

• 1.7.1 Understand that infinite limits provide information about the graph of the function near a vertical asymptote line
• 1.7.2 Algebraically determine when a limit has an answer of positive or negative infinity
• 1.7.3 Know that a limit that has an answer of positive or negative infinity technically "D.N.E."

Terminology

Define: vertical asymptote line, infinite limit