Step 1 :

Definition of limit :

if and only if and .

Step 2 :

(a)

Observe the graph :

Since the point is lies on the graph of , the value .

The value of is 0.

Step 3 : 

(b)

Observe the graph :

As x approaches 0 from the left side, the value of   tends to 1.

As x approaches 0 from the right side, the value of   tends to 1.

From the definition,

Step 4 : 

(c)

Observe the graph :

Since the point is lies on the graph of , the value .

The value of is 2.

Step 5 :

(d)

Observe the graph :

As x approaches 1 from the left side, the value of   tends to 2.

As x approaches 1 from the right side, the value of   tends to 2.

From the definition,

Solution : 

(a) The value of is 0.

(b)

(c) The value of is 2.

(d)