8. C'(0, 1] is the space of continuous functions f : [0, 1] → R with a continuous derivativef' : [0, 1] → R. Show that with the norm || f|| defined by || f|| = ||f |+ || f'||∞ the spaceC'(0, 1] is complete.

Let, fnn=1∞ be a Cauchy sequence in C10,1than for any ε>0 there exist N∈ℕ such that ∀m,n>N…

Answered: 8. C'(0, 1] is the space of continuous…

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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8. C'(0, 1] is the space of continuous functions f : [0, 1] → R with a continuous derivative f' : [0, 1] → R. Show that with the norm || f|| defined by || f|| = || f |0+|| f'|| 0, the space C'0, 1] is complete.