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4130 HOMEWORK 8
Due Tuesday May 3
(1) Let
f
n
:
A
→
R
be functions which converge uniformly on
A
to a function
f
. Let
x
0
be
a cluster point of
A
. Suppose lim
x
→
x
0
f
n
(
x
) exists for all
n
. Let
L
n
= lim
x
→
x
0
f
n
(
x
).
(a) Show that the sequence
{
L
n
}
converges.
(b) Show that lim
x
→
x
0
f
(
x
) exists and equals lim
n
→∞
L
n
.
(2) Section 7.3.4 Exercise 11.
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Unformatted text preview: (3) Find the radius of convergence of the power series f ( x ) = ∞ X n =0 ( n 2 + n + 1) x n . Find a pair of polynomials p ( x ) and q ( x ) such that f ( x ) = p ( x ) q ( x ) within its radius of convergence. 1...
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This note was uploaded on 09/22/2010 for the course MATH 413 at Cornell University (Engineering School).
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