Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
Asymptotes, Cac077, Vertical Asymptotes
License:
Creative Commons Attribution Non-Commercial
Language:
English
Media Formats:
eBook, Interactive

Education Standards (1)

Using limits to detect asymptotes modules

Overview

After completing this section, students should be able to do the following.

  • Recognize when a limit is indicating there is a vertical asymptote.
  • Evaluate the limit as xx approaches a point where there is a vertical asymptote.
  • Match graphs of functions with their equations based on vertical asymptotes.
  • Discuss what it means for a limit to equal ∞∞.
  • Define a vertical asymptote.
  • Find horizontal asymptotes using limits.
  • Produce a function with given asymptotic behavior.
  • Recognize that a curve can cross a horizontal asymptote.
  • Understand the relationship between limits and vertical asymptotes.
  • Calculate the limit as xx approaches ±∞±∞ of common functions algebraically.
  • Find the limit as xx approaches ±∞±∞ from a graph.
  • Define a horizontal asymptote.
  • Compute limits at infinity of famous functions.
  • Find vertical asymptotes of famous functions.
  • Identify horizontal asymptotes by looking at a graph.
  • Identify vertical asymptotes by looking at a graph.

Zoom out

Ximera Module

Two young mathematicians discuss what curves look like when one ``zooms out.''

Vertical asymptotes

Ximera Module

We explore functions that ``shoot to infinity'' near certain points.

Horizontal asymptotes

Ximera Module

We explore functions that behave like horizontal lines as the input grows without bound.

Slant asymptotes

Ximera Module

We explore functions that ``shoot to infinity'' at certain points in their domain.