# 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.