The limit of the function is .

 definition of limit :

,

if for every number of , there exists a  such that  whenever .

From the definition, if  then .

When .

Consider .

Graph :

Graph of the function :

Observe the graph.

The function lies in the interval .

Consider .

.

The function lies in the interval .

Compare  with .

Here  value should be a smaller positive number.

Therefore .

When .

Consider 

Graph :

Graph of the function :

Observe the graph.

The function lies in the interval .

Consider .

.

The function lies in the interval .

Compare  with .

Here  value should be a smaller positive number.

Therefore .

When  then .

When  then .