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
.