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47. (a)
lim
x
→
2‘
f
(
x
)
5
lim
x
→
2‘
1
}
1
x
}
2
5
0
(b)
lim
x
→
‘
f
(
x
)
5
lim
x
→
‘
(
2
1)
52
1
(c)
lim
x
→
0
2
f
(
x
)
5
lim
x
→
0
2
}
1
x
}52‘
(d)
lim
x
→
0
1
f
(
x
)
5
lim
x
→
0
1
(
2
1)
1
48. (a)
lim
x
→
2‘
f
(
x
)
5
lim
x
→
2‘
}
x
x
2
2
2
1
} 5
lim
x
→
2‘
}
x
x
}
5
1
(b)
lim
x
→
‘
f
(
x
)
5
lim
x
→
‘
}
x
1
2
} 5
0
(c)
lim
x
→
0
2
f
(
x
)
5
lim
x
→
0
2
}
x
x
2
2
2
1
} 5 }
0
0
2
2
2
1
} 5
2
(d)
lim
x
→
0
1
f
(
x
)
5
lim
x
→
0
1
}
x
1
2
}5‘
49.
One possible answer:
50.
One possible answer:
51.
Note that
}
g
f
1
1
(
(
x
x
)
)
/
/
f
g
2
2
(
(
x
x
)
)
}5
}
f
g
1
1
(
(
x
x
)
)
g
f
2
2
(
(
x
x
)
)
}
f
f
1
2
(
(
x
x
)
)
/
/
g
g
1
2
(
(
x
x
)
)
}
.
As
x
becomes large,
}
g
f
1
1
}
and
}
g
f
2
2
}
both approach 1. Therefore,
using the above equation,
}
g
f
1
1
/
/
f
g
2
2
}
must also approach 1.
52.
Yes. The limit of (
f
1
g
) will be the same as the limit of
g
.
This is because adding numbers that are very close to a
given real number
L
will not have a significant effect on the
value of (
f
1
g
) since the values of
g
are becoming
arbitrarily large.
53. (a)
Using 1980 as
x
5
0:
y
2.2316
x
3
1
54.7134
x
2
2
351.0933
x
1
733.2224
[0, 20] by [0, 800]
(b)
Again using 1980 as
x
5
0:
y
5
1.458561
x
4
2
60.5740
x
3
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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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