Asap plz solve all parts handwritten answer acceptable Will definitely upvote (2) Let X = C[0,4], with the usual notation and suppose X is endowed with thenorm,||||2 = ([^\f(t)1³dt) ³Consider the sequence {9}1 defined byn=10,gn(t) =(t-2),1,Verify that(i) 9n C[0, 4] for each n;(ii) {9} is a Cauchy sequence;(iii) gng as n → ∞, wheren=1if 0 ≤ t ≤ 2;if 2 ≤t≤ 2+if 2 + ² ≤ t ≤ 4.0,if 0 ≤ t ≤ 2;1,if 2 < t < 4.Conclude that C[0, 4] with ||.||2 norm is not a complete space.g(t) =

Let X = C[0,4], with the usual notation and suppose X is endowed with the norm, ||f||2 Consider the sequence {9} defined by n=1 9n(t) = = 1, = (t-2), Verify that (i) 9n C[0, 4] for each n; (ii) {9} is a Cauchy sequence; n=1 (iii) gn →g as n→∞, where (L'iscopar)¹ g(t) 0, if 0 ≤t≤ 2; if 2 < t < 4. 1, Conclude that C[0, 4] with ||.||2 norm is not a complete space. = if 0 ≤ t ≤ 2; if 2 ≤ t ≤ 2 + ²/3; if 2 + / ≤ t ≤ 4.

Let X = C[0,4], with the usual notation and suppose X is endowed with the norm, ||f||2 Consider the sequence {9} defined by n=1 9n(t) = = 1, = (t-2), Verify that (i) 9n C[0, 4] for each n; (ii) {9} is a Cauchy sequence; n=1 (iii) gn →g as n→∞, where (L'iscopar)¹ g(t) 0, if 0 ≤t≤ 2; if 2 < t < 4. 1, Conclude that C[0, 4] with ||.||2 norm is not a complete space. = if 0 ≤ t ≤ 2; if 2 ≤ t ≤ 2 + ²/3; if 2 + / ≤ t ≤ 4.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.1: Infinite Sequences And Summation Notation

Problem 72E

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