(a)

Find .

Observe the graph.

Left hand limit :

As  approaches to  from left side,  approaches to .

.

Right hand limit :

As approaches to from right side, approaches to .

.

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

. 

(b)

Find .

Observe the graph.

As tends to from left side, approaches to .

So .

(c)

Find .

Observe the graph.

As tends to from right side, approaches to .

So .

(d)

Find .

Observe the graph.

Left hand limit :

As approaches to from left side, approaches to .

.

Right hand limit : 

As approaches to from right side, approaches to .

.

Here left hand limit and right hand limit are not equal.

does not exist. 

(e)

Find .

Observe the graph that exists.

The solid dot indicates that value of the function exist at .

The value of the function at is .

So .

(a) .

(b) .

(c) .

(d) does not exist.

(e) .