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66. (a)
Note that 2 mi
5
10,560 ft, so there are
ˇ
8
w
0
w
0
w
2
w
1
w
x
w
2
w
feet of river cable at $180 per foot and (10,560
2
x
)
feet of land cable at $100 per foot. The cost is
C
(
x
)
5
180
ˇ
8
w
0
w
0
w
2
w
1
w
x
w
2
w
1
100(10,560
2
x
)
(b)
C
(0)
5
$1,200,000
C
(500)
<
$1,175,812
C
(1000)
<
$1,186,512
C
(1500)
5
$1,212,000
C
(2000)
<
$1,243,732
C
(2500)
<
$1,278,479
C
(3000)
<
$1,314,870
Values beyond this are all larger. It would appear that
the least expensive location is less than 2000 ft from
point
P.
67. (a)
[
2
3, 3] by [
2
1, 3]
(b)
Domain of
y
1
: [0,
‘
)
Domain of
y
2
:(
2‘
,1]
Domain of
y
3
: [0, 1]
(c)
The functions
y
1
2
y
2
,
y
2
2
y
1
, and
y
1
?
y
2
all have
domain [0, 1], the same as the domain of
y
1
1
y
2
found
in part (b).
Domain of
}
y
y
1
2
}
: [0, 1)
Domain of
}
y
y
2
1
}
: (0, 1]
(d)
The domain of a sum, difference, or product of two
functions is the intersection of their domains.
The domain of a quotient of two functions is the
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 Spring '08
 GERMAN

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