Definition of limits at infinity :

Let  be a real number.

1. The statement  means that for each  there exists an  such that   whenever .

2. The statement  means that for each  there exists an  such that   whenever .

The limit expression is.

Here  and .

.

 whenever .

Let .

For , .

.

Thus, for each  there exists an  such that  whenever .

The statement  is proved.