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-(1/t)2 for t0 2.65. If f(t) = show that f(n) (0) = 0 for all n for t= 0'

-(1/t)2 for t0 2.65. If f(t) = show that f(n) (0) = 0 for all n for t= 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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Please rigorously prove this using mathematical induction and the difference quotient.

-(1/t)2 for t0 2.65. If f(t) = show that f(n) (0) = 0 for all n for t= 0'
Transcribed Image Text:-(1/t)2 for t0 2.65. If f(t) = show that f(n) (0) = 0 for all n for t= 0'
Expert Solution
Step 1
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Step 2
Heie hJesivative Ptn-2) ,2th-1) +(-1) (0) nt conlants i toue fo tohee A6 n the- t ort ement k- If this 3 f+) () 31 above eq" D 6.0 4 t o in Sukstitute the (-1 C Assume 1 the equ. ain ubtitute B. + (k) X e Sukstitute t +2 12 1 ** 3 +C- B.D t (-)AD B.0 ( C- ( 8.0 . + D -
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