(a)

where .

Observe the graph:

As  tends to  from right hand side,  approaches to .

.

(b)

where .

Observe the graph:

As tends to from left hand side,  approaches to .

.

(c)

where .

Observe the graph:

Since the left hand limit and right hand limit are equal, the limit exists.

.

The function is continuous over the interval .

(a) .

(b) .

(c) .

The function is continuous on .