1. A function f is defined by 1 2 = + 3 4 f(x)= x + 3 32 33 34 for all in the interval of convergence for the x (a) Find the radius of convergence for the po (b) Find the interval of convergence for the F (c) Find the power series representation for (d) Find the power series representation for + -x2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. A function f is defined by
1 2
f(x)
3
4
+
n+1
3
32x+
33x² +
342°+
+
3n+1
for all x in the interval of convergence for the
n=0
power series.
(a) Find the radius of convergence for the
power series.
(b) Find the interval of convergence for the power series.
(c) Find the power series representation for f'(x) and state its radius of convergence.
(d) Find the power series representation
for
[ f(₂
f(x)dx.
-
-Xn
+. =
n+1
3n+1
-xn
Transcribed Image Text:1. A function f is defined by 1 2 f(x) 3 4 + n+1 3 32x+ 33x² + 342°+ + 3n+1 for all x in the interval of convergence for the n=0 power series. (a) Find the radius of convergence for the power series. (b) Find the interval of convergence for the power series. (c) Find the power series representation for f'(x) and state its radius of convergence. (d) Find the power series representation for [ f(₂ f(x)dx. - -Xn +. = n+1 3n+1 -xn
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