A function assigns a value given any point . We say that a function has a limit at a point if gets closer and closer to as moves closer and closer to . A more formal definition of is: for each , there exists a such that whenever . Note that depends on : "You give me an and I'll find you a ".
The graphic enables you to examine the limit of as approaches 2. The limit is equal to 3. Note the interplay between the values and , as described above.