Getting Closer

Limits and holes

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 is the value a function approaches, not necessarily its value at the point.
• For $\frac00$ forms, simplify (for example, factor and cancel) first.
• If the left and right limits differ, the limit doesn’t exist.

Steps

1. A function with a hole
2. Cancel and substitute
3. A cubic hole
4. Redefine the point
5. A square-root hole
6. Different sides