Consider the sequence of functions {fn}nen, wherenxfn(z) =Va € [1, 10].1+ nx'(a) Find the pointwise limit of the sequence {f} on the interval [1, 10].(b) Show that the convergence is uniform..10(c) Evaluate lim f. fn(x) dx.12→∞0

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Answered: Consider the sequence of functions…

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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Consider the sequence of functions {fn}nen, where nx fn(z) = Va € [1, 10]. 1+ nx' (a) Find the pointwise limit of the sequence {f} on the interval [1, 10]. (b) Show that the convergence is uniform. .10 (c) Evaluate lim f. fn(x) dx. 12→∞0