154
Solutions
to
Exercises
Therefore,
f(x)
+
10xf(x)
+
25x
2
f(x)
=
ao
+
(al
+
lOao)x
+
(a2
+
lOal
+
25ao)x2
+ ... +
(an
+
lOanl
+
25an_2)X
n
+
....
So
f(x)(l
+
lOx
+
25x
2
)
=
1
+
35x.
Therefore,
1
f(x)
=
(1
+
5X)2
(1
+
35x)
=
(1
+
2(
5x)
+ ... +
(n
+
1)(
5xt
+ ...
)(1
+
35x)
=
1
+
25x

275x
2
+ ... +
[(n
+
1)(
5t
+
n(
5t
1
(35)]xn
+ ...
=
1
+
25x

275x
2
+ ... +
[(1

6n)(
_5)n]xn
+ ...
and
so
an
=
(1

6n)(
_5)n.
11.
[BB]
f(x)
ao
+
alX
+
a2x2
+
a3x3
+
+
anx
n
+
+
2a
n
_lX
n
+
+
an_2
Xn
+
+
2an_3
Xn
+
2xf(x)
2aox
+
2alX2
+
2a2x3
+
x
2
f(x)
aox
2
+
alx
3
+
2x
3
f(x
2aox3
+
Therefore,
f(x)

2xf(x)

x
2
f(x)
+
2x
3
f(x)
=
ao
+
(al

2ao)x
+
(a2

2al

ao)x
2
+
(a3

2a2

al
+
2ao)x3
+ ... +
(an

2an
l

an
2
+
2an_3)X
n
+ ...
=
1
+
x

x
2
since
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 Summer '10
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 Graph Theory, Trigraph, Zagreb, Zagreb bypass, Adrenergic receptor, Xn

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