The limit of the function are and .

(a)

Construct the table with nearest value of from left side, to estimate the value of :

Observe the table.

The value of at is .

As tends to from left side, approaches to large negative number.

So .

Construct the table with nearest value of from right side, to estimate the value of :

Observe the table.

The value of at is .

As tends to from right side, approaches to large positive number.

So .

(b)

The limit of the function is.

If closes to but smaller than , then the denominator is a small negative number.

So the function gets a large negative number.

.

The limit of the function is.

If closes to but larger than , then the denominator is a small positive number.

So the function gets a large positive number.

.

(c)

Graph :

Graph the function :

Observe the graph.

As tends to from left side, approaches to .

So .

As tends to from right side, approaches to .

So .

(a) and .

(c) Graph of the function is

.