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3. Is it possible for a power series centered at 0 to converge for x = 1, diverge for x = 2, and converge for x = 3? Why or why not? 4. Find a power series representation for f(x) = 3x5 1+ 2x³ centered at 0. For which values of r is it valid?

3. Is it possible for a power series centered at 0 to converge for x = 1, diverge for x = 2, and converge for x = 3? Why or why not? 4. Find a power series representation for f(x) = 3x5 1+ 2x³ centered at 0. For which values of r is it valid?

Advanced Engineering Mathematics
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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3. Is it possible for a power series centered at 0 to converge for x = 1, diverge for x = 2, and converge for x = 3? Why or why not? 4. Find a power series representation for f(x) = 325 1+ 2x³ centered at 0. For which values of r is it valid?
Transcribed Image Text:3. Is it possible for a power series centered at 0 to converge for x = 1, diverge for x = 2, and converge for x = 3? Why or why not? 4. Find a power series representation for f(x) = 325 1+ 2x³ centered at 0. For which values of r is it valid?
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