To remove the discontinuity at
, we need to find the new value
should be assigned.
Given the function
:

To remove the discontinuity at
, we need to ensure that the left-hand limit and the right-hand limit of
at
are equal.
The left-hand limit is obtained by evaluating
as
approaches
from the left:

The right-hand limit is obtained by evaluating
as
approaches
from the right:

Since the left-hand limit and the right-hand limit are both equal to
, we can assign
the value of
to remove the discontinuity.
Therefore, the new value for
should be
.

♥️
