Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
Asymptotes, Cac077, Vertical Asymptotes
Language:
English
Media Formats:
eBook, Interactive

# 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.