For a constants , define:
If are fixed, find all values for such that is continuous at .
By the definition of continuity of a function at a point, we know that is continuous at means is defined at , and .
Since and are defined for all , we know that is defined at for all . So, we must then find values of such that
From the definition of , we know
Then, we evaluate the limit as through values greater than (since the limit as through values less than is since is a continuous function, and for values less than , ),
Thus, for to be continuous at we must have,
If , then we have