Discuss the continuity of the function , where is defined by:

Solution: The provided function is

In interval,

As a result, is continuous in this interval.

At ,

Left Hand Limit =
and R.H.L.

Since, L.H.L. R.H.L.

As a result, is discontinuous at .

At ,
Left Hand Limit.
and Right Hand Limit

Since, L.H.L. R.H.L. As a result, is discontinuous at

Hence, is discontinuous at and