This is an exercise on the definition of
continuity
:

A function f is continuous on a point x_{0}, if:

For all > 0, there exists a > 0, such that
|x-x_{0}| implies
|f (x)-f (x_{0})| .

Given a concret function (who is continuous), a x_{0} and a > 0,
you have to find a > 0 which verifies the above condition. And you
will be noted according to this : more it is close to the best possible
value, better will be your note.