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Limits

Sarah Miller

Sarah Miller

6 min read

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Study Guide Overview

This study guide covers infinite limits and limits at infinity. It explains the concepts of infinite limits and their connection to vertical asymptotes. It also discusses limits at infinity and their relationship with horizontal asymptotes. The guide includes worked examples, practice questions, and a glossary of key terms like vertical asymptote and horizontal asymptote.

Study Notes on Infinite Limits and Limits at Infinity

Table of Contents

  1. Infinite Limits
  2. Limits at Infinity
  3. Practice Questions
  4. Glossary
  5. Summary and Key Takeaways

Infinite Limits

What is an Infinite Limit?

Infinite limits occur when the values of a function become unbounded (either positively or negatively) as xx approaches a specific value.

Key Concept

If the value of a function ff increases without bound as xx approaches some value cc, we write: lim⁡x→cf(x)=∞\lim_{{x \to c}} f(x) = \infty

If the value of a function ff decreases without bound as xx approaches some value cc, we write: lim⁡x→cf(x)=−∞\lim_{{x \to c}} f(x) = -\infty

For example: lim⁡_x→01x2=∞\lim\_{{x \to 0}} \frac{1}{x^2} = \infty lim⁡_x→0(−1x2)=−∞\lim\_{{x \to 0}} \left(-\frac{1}{x^2}\right) = -\infty One-sided limits can be different. For example: $$ \lim_{{x...
Previous Topic - Definition of a LimitNext Topic - Properties of Limits

Question 1 of 12

What does the notation lim⁡x→cf(x)=∞\lim_{x \to c} f(x) = \infty signify about the function f(x)f(x) as xx approaches cc?

The function approaches zero

The function decreases without bound

The function increases without bound

The function approaches a finite value