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Let Se-1/2 if r + 0 f(x) = if a = 0 Show that f has derivatives of all orders at 0 and that f (m) (0) = 0 for all n E N. Thus the Taylor series for f at æo = 0 does not represent f for any a + 0.

Let Se-1/2 if r + 0 f(x) = if a = 0 Show that f has derivatives of all orders at 0 and that f (m) (0) = 0 for all n E N. Thus the Taylor series for f at æo = 0 does not represent f for any a + 0.

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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Let Se-1/2 if r + 0 f(x) = if a = 0 Show that f has derivatives of all orders at 0 and that f (m) (0) = 0 for all n E N. Thus the Taylor series for f at æo = 0 does not represent f for any a + 0.
Transcribed Image Text:Let Se-1/2 if r + 0 f(x) = if a = 0 Show that f has derivatives of all orders at 0 and that f (m) (0) = 0 for all n E N. Thus the Taylor series for f at æo = 0 does not represent f for any a + 0.
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