Given constants define:
If are fixed find all values of
such that
is continuous at
.
By the definition of continuity, we know that continuous at
means that
is defined and
. Since
and
are defined for all
, we know that
is defined for every
. Then, to show that it is continuous we must show
From the definition of we know
Then, taking the limit as approaches
from the right (since
since
is continuous and
as
approaches
from the left),
So, we must have
If then,