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(b)
The average speed over the interval from time
t
5
3 to
time 3
1
h
is
}
D
D
y
t
}
55
}
4.9(6
h
h
1
h
2
)
}
5
29.4
1
4.9
h
Since lim
h
→0
(29.4
1
4.9
h
)
5
29.4, the instantaneous
speed is 29.4 m/sec.
58. (a)
y
5
gt
2
20
5
g
(4
2
)
g
5 }
2
1
0
6
} 5 }
5
4
}
or 1.25
(b)
Average speed
5 }
2
4
0
} 5
5 m/sec
(c)
If the rock had not been stopped, its average speed over
the interval from time
t
5
4 to time
t
5
4
1
h
is
}
D
D
y
t
}
}
1.25(8
h
h
1
h
2
)
}
5
10
1
1.25
h
Since lim
h
→0
(10
1
1.25
h
)
5
10, the instantaneous speed
is 10 m/sec.
59. (a)
(b)
The limit appears to be 0.
60. (a)
(b)
There is no clear indication of a limit.
61. (a)
(b)
The limit appears to be approximately 2.3.
62. (a)
(b)
The limit appears to be 0.
63. (a)
Because the righthand limit at zero depends only on
the values of the function for positive
x
values near
zero.
(b)
Area of
n
OAP
5 }
1
2
}
(base)(height)
5 }
1
2
}
(1)(sin
u
)
5 }
sin
2
u
}
Area of sector
5
}
(angle)(
2
radius)
2
}5}
u
(
2
1)
2
} 5 }
u
2
}
Area of
n
OAT
5 }
1
2
}
(base)(height)
5 }
1
2
}
(1)(tan
u
)
5 }
tan
2
u
}
(c)
This is how the areas of the three regions compare.
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 Spring '08
 GERMAN

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