(a)

The function is , .

Check the continuity of the function at .

Substitute  in the above function.

 is undefined.

Left hand limit :

Right hand limit :

Left hand limit and right hand limit are equal, limit exist.

.

Limit exist at .

But .

Therefore the function  has removable discontinuous at .

Find the function  by eliminating discontinuity at .

The new function is .

(b)

The function is , .

Check the continuity of the function at .

Substitute  in the above function.

 is undefined.

Left hand limit :

Right hand limit :

Left hand limit and right hand limit are equal, limit exist.

.

Limit exist at .

But .

Therefore the function  has removable discontinuous at .

Find the function  by eliminating discontinuity at .

The new function is .

(b)

The function is , .

Check the continuity of the function at .

Graph :

Graph the function  :

Observe the graph.

.

Observe the graph.

Left hand limit :

As  tends to  from left side,  approaches to .

.

Right hand limit :

As  tends to  from left side,  approaches to .

.

Left hand limit and right hand limit are not equal, limit does not exist.

.

Limit  does not exist at  and .

Therefore the function  is discontinuous at .

(a) .

(b)  .