Example 4.6.2
Take

,

and

. For any real number in

, we have

.
Moreover,
and
have both a positive infinite limit at
, thus
has a positive infinite limit at
(see Figure fig example sandwich 1).
Example 4.6.4
We know that the sine function is bounded on

, thus the
function

is bounded on any pointed
neighborhood of 0. Moreover

. Thus

. See Figure fig example sandwich 2.