Limits at Infinity

Where functions settle down

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• A limit at infinity describes where f(x) settles for large x: a horizontal asymptote.
• For rational functions, compare the leading terms.
• ε–N: for any tolerance, beyond some N the function stays that close.

Steps

1. What happens far out?
2. Leading terms
3. Close enough?
4. Which goes where?
5. An asymptote
6. A difference of large numbers