The function is
.
Observe the given graph.
\(a) Find
.
As
tends to
from left hand side,
approaches to
.
As
tends to
from right hand side,
approaches to
.
The limit from left hand side and right hand side are not equal and undefined.
\Limit does not exist.
\
does not exist.
(b) Find
.
As
tends to
from left hand side,
approaches to
.
As
tends to
from right hand side,
approaches to
.
Since the limit from left hand side and right hand side are equal, limit exist.
\
.
.
agree at all points other than
and
.
Rewrite the function as
.
Cancel the common terms.
\
. The simpler form of function is
.
and
agree at all points other than
and
.
(a)
does not exist.
(b)
.
and
agree at all points other than
and
.