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19. (For students who have studied calculus) Use mathemati- cal induction, the product rule from calculus, and the facts that dx (r)p = 1 and that x*+1 = x-x* to prove that for all d(x*) integers n > 1, = nx*-!. dx

19. (For students who have studied calculus) Use mathemati- cal induction, the product rule from calculus, and the facts that dx (r)p = 1 and that x*+1 = x-x* to prove that for all d(x*) integers n > 1, = nx*-!. dx

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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19. (For students who have studied calculus) Use mathemati- cal induction, the product rule from calculus, and the facts d(x) that dx 1 and that x*+! =x.x* to prove that for all d(x") integers n > 1, = nx" -1. dx
Transcribed Image Text:19. (For students who have studied calculus) Use mathemati- cal induction, the product rule from calculus, and the facts d(x) that dx 1 and that x*+! =x.x* to prove that for all d(x") integers n > 1, = nx" -1. dx
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