This preview shows page 1. Sign up to view the full content.
46.
Since
V
5
p
r
2
h
, we have
}
d
d
V
r
} 5
2
p
rh
, and
dV
5
2
p
rh dr
.
We want
)
dV
)
#
0.001
V
, which gives
)
2
p
rh dr
)
#
0.001
p
r
2
h
, or
)
dr
)
#
0.0005
r
. The variation of
the radius should not exceed
}
20
1
00
}
of the ideal radius, that
is, 0.05% of the ideal radius.
47.
We have
}
d
d
W
g
}52
bg
2
2
, so
dW
52
bg
2
2
dg
.
Then
}
d
d
W
W
m
ea
o
r
o
th
n
} 5
}
2
2
b
b
(
(
5
3
.
2
2
)
)
2
2
2
2
d
d
g
g
}5}
5
3
.
2
2
2
2
}
<
37.87. The ratio is
about 37.87 to 1.
48. (a)
Note that
T
5
2
p
L
1/2
g
2
1/2
, so
}
d
d
T
g
p
L
1/2
g
2
3/2
and
dT
p
L
1/2
g
2
3/2
dg
.
(b)
Note that
dT
and
dg
have opposite signs. Thus, if
g
increases,
T
decreases and the clock speeds up.
(c)
2
p
L
1/2
g
2
3/2
dg
5
dT
2
p
(100)
1/2
(980)
2
3/2
dg
5
0.001
dg
<
2
0.9765
Since
dg
<
2
0.9765,
g
<
980
2
0.9765
5
979.0235.
49.
If
f
9
(
x
)
±
0, we have
x
2
5
x
1
2 }
f
f
9
(
(
x
x
1
1
)
)
} 5
x
1
2 }
f
9
(
0
x
1
)
} 5
x
1
.
Therefore
x
2
5
x
1
, and all later approximations are also
equal to
x
1
.
50.
If
x
1
5
h
, then
f
9
(
x
1
)
5 }
2
h
1
1/2
}
and
x
2
5
h
2
5
h
2
2
h
h
. If
x
1
h
, then
f
9
(
x
1
)
52}
2
ˇ
1
h
w
}
and
x
2
h
25
2
h
1
2
h
5
h
[
2
3, 3] by [
2
0.5, 2]
51.
Note that
f
9
(
x
)
5 }
1
3
}
x
2
2/3
and so
x
n
1
1
5
x
n
2 }
f
f
9
(
(
x
x
n
n
)
)
}
5
This is the end of the preview. Sign up
to
access the rest of the document.
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

Click to edit the document details