Pham, Quoc – Homework 10 – Due: Apr 4 2007, 3:00 am – Inst: Eric Katerman
1
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printout
should
have
16
questions.
Multiplechoice questions may continue on
the next column or page – fnd all choices
beFore answering.
The due time is Central
time.
001
(part 1 oF 1) 10 points
±ind a Formula For the general term
a
n
oF
the sequence
n
2
,
6
,
10
,
14
, ...
o
assuming that the pattern oF the frst Few
terms continues.
1.
a
n
= 3
n

1
2.
a
n
= 5
n

3
3.
a
n
=
n
+ 4
4.
a
n
=
n
+ 3
5.
a
n
= 4
n

2
correct
Explanation:
In the sequence
n
2
,
6
,
10
,
14
, ...
o
each term is larger than the preceding one by
4, so
a
n
=
a
1
+
d
(
n

1) = 2 + 4(
n

1)
.
Consequently,
a
n
= 4
n

2
.
keywords:
002
(part 1 oF 1) 10 points
±ind a Formula For the general term
a
n
oF
the sequence
n
1
,

2
5
,
4
25
,

8
125
, ...
o
assuming that the pattern oF the frst Few
terms continues.
1.
a
n
=

‡
1
2
·
n
2.
a
n
=
‡

2
5
·
n

1
correct
3.
a
n
=

‡
2
5
·
n
4.
a
n
=

‡
5
2
·
n
5.
a
n
=
‡

5
2
·
n

1
6.
a
n
=
‡

1
2
·
n

1
Explanation:
In the sequence
n
1
,

2
5
,
4
25
,

8
125
, ...
o
each term is

2
5
times the preceeding one,
i.e.
,
a
n
=
‡

2
5
·
a
n

1
.
Consequently,
a
n
=
‡

2
5
·
n

1
since
a
1
= 1.
keywords: sequence, exponential
003
(part 1 oF 1) 10 points
Determine iF the sequence
{
a
n
}
converges,
and iF it does, fnd its limit when
a
n
=
5
n
5

4
n
3
+ 3
5
n
4
+
n
2
+ 1
.
1.
limit = 1
2.
the sequence diverges
correct
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View Full DocumentPham, Quoc – Homework 10 – Due: Apr 4 2007, 3:00 am – Inst: Eric Katerman
2
3.
limit = 0
4.
limit =

4
5.
limit = 3
Explanation:
After division by
n
4
we see that
a
n
=
5
n

4
n
+
3
n
4
5 +
1
n
2
+
1
n
4
.
Now
4
n
,
3
n
4
,
1
n
2
,
1
n
4
→
0
as
n
→ ∞
; in particular, the denominator
converges and has limit 5
6
= 0.
Thus by
properties of limits
{
a
n
}
diverges
since the sequence
{
5
n
}
diverges.
keywords:
004
(part 1 of 1) 10 points
Determine whether the sequence
{
a
n
}
con
verges or diverges when
a
n
=
10
n
2
2
n
+ 1

5
n
2
+ 2
n
+ 1
,
and if it does, Fnd its limit
1.
limit =
5
2
correct
2.
limit =
5
6
3.
the sequence diverges
4.
limit =
5
4
5.
limit = 0
Explanation:
After bringing the two terms to a common
denominator we see that
a
n
=
10
n
3
+ 10
n
2

(2
n
+ 1)
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 Spring '08
 RAdin
 Calculus, Limit, Limit of a function, Natural logarithm

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