4) Give an example, if possible, of power series with the following properties a) centered at Zo=3i, with radius of convergence R= 7 b) centered at Zo=1 and convergent for all z with Imz≤9, but divergent for all z with Im Z >4 c) centered at Zo=0 and convergent for all z with Rez=8, but divergent for all other ZEC.
4) Give an example, if possible, of power series with the following properties a) centered at Zo=3i, with radius of convergence R= 7 b) centered at Zo=1 and convergent for all z with Imz≤9, but divergent for all z with Im Z >4 c) centered at Zo=0 and convergent for all z with Rez=8, but divergent for all other ZEC.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 49E
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Questions 4a and 4c handwritten please
Transcribed Image Text:4) Give
an
properties
example, if possible, of power series with the following
a) centered at Zo=3i, with radius of convergence R = 7
(b) centered at Zo=1 and convergent for all z with Im764, but
divergent for all z with Im Z >4.
c) centered at Zo=0 and convergent for all & with Rez = 8, but
divergent for all other ZEC.
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