Example:

Find the limit of the function:

as x approaches 1.

Solution:

Again, we derive from the table that as x represents values closer and closer to 1, the value of the function gets closer and closer to 4. Here we can say that the limit of the function as x approaches 1 is 4.

Substituting 1 for x in the previous rule of correspondence gives us:

That is an indefinite quantity. Thus, although the function does not have a value at x=1, it has a limit at that point.