Step 1:

The limit function is .

The function is .

Definition of the limit :

Let be a function defined on an open interval containing and let be a real number.

The statement is

means that for each there exists a such that if , then .

Step 2:

From the definition :

Step 3:

For :

Find such that    whenever .

Definition of limit:

Let be a function defined on an open interval containing and let be a real number.

The statement  

means that for each , there exists a  such that , then .

Step 4:

  whenever .

\ \

We need to establish a connection between   and .

Consider

Since ,

Compare the above with , then .

Step 5:

For :

Find such that    whenever .

  whenever .

We need to establish a connection between   and .

Consider

Since ,

Compare the above with , then .

Solution:

(a) and .

(b) .

     .