help? plz . lc

Question

Answer 1

(14)

Step 1:

The function is and .

Definition of continuity :

A function is continuous at , if then it should satisfy three conditions :

(1) is defined.

(2) exists.

(3) .

Condition (1): is defined.

If then .

Substitute in the function.

.

is defined.

Step 2:

Condition (2): exists.

.

exists.

Comments

Contd....

Step 3:

Condition (3): .

and .

.

The three conditions of continuity are satisfied, hence the function is continuous.

The function is continuous at .

Solution :

The function is continuous at .

Answer 2

(15)

Step 1:

The function is and .

Definition of continuity :

A function is continuous at , if then it should satisfy three conditions :

(1) is defined.

(2) exists.

(3) .

Condition (1): is defined.

If then .

Substitute in above function.

.

is defined.

Step 2:

Condition (2): exists.

Left hand limit :

If then .

.

Right hand limit :

If then .

.

Comments

Contd....

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

does not exist.

Here limit does not exist at .

The condition (2) of continuity is not satisfied, hence the function is discontinuous.

The function is discontinuous at .

Solution :

The function is discontinuous at .