The limit of the function is .

 definition of limit :

,

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

Consider .

Consider .

.

Observe the relation between  and  .

.

 must be in terms of , with no other variables depending on it.

Since .

.

 value is minimum, when  is maximum.

From the above, the restrictions are  and .

Then the obtained relation is .

Verification :

For every number of  if  then .

Consider .

Now consider  .

.