22. (a)
a
0
5
1
a
1
5 }
3
1
}
a
0
5
3
?
1
5
3
a
2
5 }
3
2
}
a
1
5 }
3
2
}
?
3
5 }
9
2
}
a
3
5 }
3
3
}
a
2
5
a
2
5 }
9
2
}
Since each term is obtained by multiplying the previous
term by
}
3
n
}
,
a
n
5 }
3
n
n
!
}
.
∑
‘
n
5
0
a
n
x
n
5
1
1
3
x
1 }
9
2
}
x
2
1 }
9
2
}
x
3
1
…
1 }
3
n
n
!
}
x
n
1
…
(b)
Since the series can be written as
∑
‘
n
5
0
}
(3
n
x
!
)
n
}
, it represents
the function
f
(
x
)
5
e
3
x
.
(c)
f
9
(1)
5
3
e
3
x
)
x
5
1
5
3
e
3
23.
First, note that cos 18
<
0.6603.
Using cos
x
5
∑
‘
n
5
0
(
2
1)
n
}
(2
x
n
2
n
)!
}
, enter the following twostep
commands on your home screen and continue to hit
ENTER.
The sum corresponding to
N
5
25 is about 0.6582 (not
withing 0.001 of exact value), and the sum corresponding
to
N
5
26 is about 0.6606, which is within 0.001 of the
exact value. Since we began with
N
5
0, it takes a total of
27 terms (or, up to and including the 52nd degree term).
24.
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 Spring '08
 GERMAN
 Maclaurin Series, Taylor Series, exact value, tan tan, degree term

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