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