Suppose f is defined on the open interval I and a E I. The Taylor polynomial Pak is well defined provided merely that f is of class Ck-1 on I and f(k)(a) exists. Show that under these hypotheses, the remainder Ra,k = f - Pak still satisfies limp-0 Ra,k(h)/hk = 0. (Hint: Apply l'Hôpital's rule k – 1 times, then recall precisely what it means for flk)(a) to exist.) %3D

Suppose f is defined on the open interval I and a E I. The Taylor polynomial Pak is well defined provided merely that f is of class Ck-1 on I and f(k)(a) exists. Show that under these hypotheses, the remainder Ra,k = f - Pak still satisfies limp-0 Ra,k(h)/hk = 0. (Hint: Apply l'Hôpital's rule k – 1 times, then recall precisely what it means for flk)(a) to exist.) %3D

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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