Example

Let f be the function defined by:

Find:

Solution

The function f is a rational function, but 1/3 is not an element of its domain. Hence, we cannot simply substitute in the previous rule of correspondence to get the limit, but using the theorem we have just learnt will make the answer easy.

First, note that the function can be rewritten in the form

Now, consider the function , for all . The two functions f and g have the same value at all real numbers except 1/3. Thus, we can say that:

That is by direct substitution, because g is a polynomial function.

We can answer the problem shortly by saying: