Math / Introduction to Real Analysis 3 / Chapter 10.2 / Problem 18

Introduction to Real Analysis | 3rd Edition | ISBN: 9780471321484 | Authors: Robert G. Bartle, Donald R. Sherbert

Let gn(x) := -1 for x E [-1, -I/n), let gn(x) := nx for x E [-I/n, I/n] and let gn(x) :=

Chapter 10, Problem 18

(choose chapter or problem)

Let gn(x) := -1 for x E [-1, -I/n), let gn(x) := nx for x E [-I/n, I/n] and let gn(x) := 1for x E (1In, 1]. Show that IIgm - gn II ~ 0 as m, n ~ 00, so that the Completeness Theorem10.2.12 implies that there exists g E [-1, 1] such that (gn) converges to gin [-1,1]. Findsuch a function g.

Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.

Becoming a subscriber
Or look for another answer

Let gn(x) := -1 for x E [-1, -I/n), let gn(x) := nx for x E [-I/n, I/n] and let gn(x) :=

Login

Register

Let gn(x) := -1 for x E [-1, -I/n), let gn(x) := nx for x E [-I/n, I/n] and let gn(x) :=

Login

Register

Reset password