Step 1:

The function is .

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 2:

  whenever .

We need to establish a connection between   and .

Consider

Subtract from each side.

Since ,

Compare the above with , then .

Solution:

.

Step 1:

(2)

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 2:

  whenever .

Consider

Observe the graph:

Compare and .

Lower values:

Upper value:

The values of are 0.1 and 0.3

Solution:

The values of are 0.1 and 0.3.