(a)

Theorem  :

If  is a continuous function at , then , where  is a constant.

The limit of the function is .

Definition of continuity :

The function  is a continuous at , then .

.

(b)

Theorem  :

If  and  are continuous function at , then .

The limit of the function is .

Definition of continuity :

The functions  and  is a continuous at , then  and .

.

(a) .

(b) .