(a)

The limit is .

Consider .

Graph:

Graph the function .

Observe the graph:

The graph of the function approaches to zero as tends to .

.

(b)

Use the graph of the sequence.

Definition 2:

A sequence has the limit and , if for every ther is a corresponding integer such that

if then .

Here from (a): .

Case (i): For .

According to definition, the graph point should lie between and .

Graph:

Graph the function .

Draw the line .

Observe the graph:

The graph of the function approaches to as tends to .

Therefore, for , the value of is .

.

Case (ii): For .

According to definition, the graph point should lie between and .

Graph:

Graph the function .

Draw the line .

Observe the graph:

The graph of the function approaches to as tends to .

Therefore, for , the value of is .

.

(a) .

(b) 

For , .

For , .