suleimenov (bs26835) – FINAL REVIEW #2 – rusin – (55565)
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001
10.0points
Find the interval of convergence of the se
ries
∞
summationdisplay
n
=1
x
n
√
n
+ 4
.
1.
converges only at
x
= 0
2.
interval of cgce = [
−
1
,
1]
3.
interval of cgce = [
−
1
,
1)
4.
interval of cgce = (
−
4
,
4]
5.
interval of cgce = (
−
1
,
1)
6.
interval of cgce = [
−
4
,
4]
002
10.0points
Determine the interval of convergence of
the series
∞
summationdisplay
k
=1
(
−
1)
k

1
1
k
2
(
x
−
1)
k
.
1.
interval of convergence = [
−
2
,
0 )
2.
interval of convergence = (0
,
2 )
3.
interval of convergence = [0
,
2 ]
4.
interval of convergence = (0
,
2 ]
5.
interval of convergence = [0
,
2 )
6.
interval of convergence = (
−
2
,
0 ]
7.
interval of convergence = [
−
2
,
0 ]
8.
interval of convergence = (
−
2
,
0 )
003
10.0points
If the radius of convergence of the power
series
∞
summationdisplay
n
=0
c
n
x
n
is 36, what is the radius of convergence,
R
, of
the power series
∞
summationdisplay
n
=0
c
n
x
2
n
?
1.
R
= 6
2.
R
=
∞
3.
R
= 36
4.
R
= 0
5.
R
= 1
6.
R
=
√
6
004
10.0points
Determine the value of
f
(1) when
f
(
x
) =
x
2
2
−
2
x
3
2
4
+
3
x
5
2
6
+
. . . .
(
Hint
:
differentiate the power series expan
sion of (
x
2
+ 2
2
)

1
.)
1.
f
(1) =
4
25
2.
f
(1) =
8
25
3.
f
(1) =
1
5
4.
f
(1) =
8
5
5.
f
(1) =
1
25
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suleimenov (bs26835) – FINAL REVIEW #2 – rusin – (55565)
2
005
10.0points
Find a power series representation for the
function
f
(
y
) = ln
radicalbigg
1 + 3
y
1
−
3
y
.
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 Spring '11
 RUSIN
 Power Series, Taylor Series, vector projection

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