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| PAGE: 60 | SET: Exercises | PROBLEM: 7 |
(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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