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33.
}
d
d
P
V
} 5 }
d
d
V
}
1
}
V
n
2
R
n
T
b
} 2 }
a
V
n
2
2
}
2
52
}
d
d
V
}
(
an
2
V
2
2
)
5
}
(
0
V
2
2
n
n
R
b
T
)
2
}1
2
an
2
V
2
3
}
(
V
n
2
RT
nb
)
2
}1}
2
V
an
3
2
}
34.
}
d
d
s
t
} 5 }
d
d
t
}
(4.9
t
2
)
5
9.8
t
}
d
d
2
t
2
s
} 5 }
d
d
t
}
(9.8
t
)
5
9.8
35.
}
d
d
M
R
} 5 }
d
d
M
}
3
M
2
1
}
C
2
}
2 }
M
3
}
24
5 }
d
d
M
}
1
}
C
2
}
M
2
2 }
1
3
}
M
3
2
5
CM
2
M
2
36.
If the radius of a circle is changed by a very small amount
D
r
, the change in the area can be thought of as a very thin
strip with length given by the circumference, 2
p
r
, and
width
D
r
. Therefore, the change in the area can be thought
of as (2
p
r
)(
D
r
), which means that the change in the area
divided by the change in the radius is just 2
p
r
.
37.
If the radius of a sphere is changed by a very small amount
D
r
, the change in the volume can be thought of as a very
thin layer with an area given by the surface area, 4
p
r
2
, and
a thickness given by
D
r.
Therefore, the change in the
volume can be thought of as (4
p
r
2
)(
D
r
), which means that
the change in the volume divided by the change in the
radius is just 4
p
r
2
.
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 Fall '08
 GERMAN

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