Step 1:

The function is

Definition of Continuity:

A function is continuous at a number ,

(1) is defined.

(2) exists.

(3) .

 The function is continuous for

Consider

and

Hence .

The function is discontinuous at .

Solution:

The function is discontinuous at .

Step 1:

The function is

Definition of Continuity:

A function is continuous at a number ,

(1) is defined.

(2) exists.

(3) .

 The function is continuous for all values of .

 The function is continuous for all values of .

The function is continuous for all values of .

Consider left hand limit at

Cancel the common terms.

Consider right hand limit at

As the right hand limit and the left hand limit are equal, limit exists at .

.

Step 2:

Consider left hand limit at .

Consider right hand limit at

As the right hand limit and the left hand limit are equal, limit exists at .

.

The function is continuous for all values of .

Solution:

The function is continuous for all values of .