As we substitute values in for x we discover that the limit does not exist because value of x<0 give us an f(x) of -1 and values of x>0 give us an f(x) value of 1.


Remember the f(x) value is the limit not the x value!

However in some scientific and business situations we are only interested in what the limit is as x approaches a number from one side.  So in the following limit, which is the same as the one above, we are only going to use values of x > 0 and this will give us what is called a limit from the right. So if you think of the number line the values of x are to the right of zero and hence the name “limit from the right”             The limit f(x) is, according to the above chart, 1.  The limit from the left is written

                         and in this case is -1