(a)
Find .
Observe the graph.
As tends to from left side, approaches to .
So .
(b)
Find .
Observe the graph.
As tends to from right side, approaches to .
So .
(c)
Find .
Observe the graph.
Left hand limit .
As approaches to from left side, approaches to .
.
Right hand limit .
As approaches to from right side, approaches to .
.
Left hand limit and right hand limit are not equal, does not exist.
(d)
Find .
Observe the graph.
As tends to from left side, approaches to .
So .
(e)
Find .
Observe the graph.
As tends to from right side, approaches to .
So .
(f)
Find .
Observe the graph.
Left hand limit :
As approaches to from left side, approaches to .
So .
Right hand limit :
As approaches to from right side, approaches to .
So .
Left hand limit and right hand limit are not equal, does not exist.
does not exist.
(g)
Find .
Observe the graph that exists.
The solid dot indicates that value of the function exist at .
The value of the function at is .
So .
(h)
Find .
Observe the graph.
Left hand limit :
As approaches to from left side, approaches to .
.
Right hand limit :
As approaches to from right side, approaches to .
.
Left hand limit and right hand limit are equal, is exist.
.
(a) .
(b) .
(c) does not exist.
(d) .
(e) .
(f) does not exist.
(g) .
(h) .
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