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19.
[
2
3, 6] by [
2
1, 5]
(a)
x
5
2
(b)
Not removable, the onesided limits are different.
20.
[
2
3, 6] by [
2
1, 5]
(a)
x
5
2
(b)
Removable, assign the value 1 to
f
(2).
21.
[
2
5, 5] by [
2
4, 8]
(a)
x
5
1
(b)
Not removable, it’s an infinite discontinuity.
22.
[
2
4.7, 4.7] by [
2
3.1, 3.1]
(a)
x
52
1
(b)
Removable, assign the value 0 to
f
(
2
1).
23. (a)
All points not in the domain along with
x
5
0, 1
(b)
x
5
0 is a removable discontinuity, assign
f
(0)
5
0.
x
5
1 is not removable, the onesided limits are
different.
24. (a)
All points not in the domain along with
x
5
1, 2
(b)
x
5
1 is not removable, the onesided limits are
different.
x
5
2 is a removable discontinuity, assign
f
(2)
5
1.
25.
For
x
±2
3,
f
(
x
)
5 }
x
x
2
1
2
3
9
} 5
}
(
x
1
x
3
1
)(
x
3
2
3)
}5
x
2
3.
The extended function is
y
5
x
2
3.
26.
For
x
±
1,
f
(
x
)
5 }
x
x
3
2
2
2
1
1
}
5
5
}
x
2
x
1
1
x
1
1
1
}
.
The extended function is
y
5
}
x
2
x
1
1
x
1
1
1
}
.
27.
Since lim
x
→
0
}
sin
x
x
} 5
1, the extended function is
y
5
h
28.
Since lim
x
→
0
}
sin
x
4
x
} 5
4 lim
x
→
0
}
sin
4
x
4
x
} 5
4(1)
5
4, the extended
function is
y
5
h
29.
For
x
±
4 (and
x
.
0),
f
(
x
)
5
}
ˇ
x
x
w
2
2
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.
 Spring '08
 GERMAN

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