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Show that if I and g are uniformly continuous on a subset A of R, then I+ g is uniformly

Introduction to Real Analysis | 3rd Edition | ISBN: 9780471321484 | Authors: Robert G. Bartle, Donald R. Sherbert ISBN: 9780471321484 424

Solution for problem 5 Chapter 5.4

Introduction to Real Analysis | 3rd Edition

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

Introduction to Real Analysis | 3rd Edition

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Problem 5

Show that if I and g are uniformly continuous on a subset A of R, then I+ g is uniformly continuous on A.

Step-by-Step Solution:
Step 1 of 3

Psychology of Learning – Choice + More on Reinforcement Self­control ­ Sometimes we have to make choices between immediate rewards, and awards that are delayed but also better. This is an issue of “self­control vs. impulsivity.” ­ What are some ways we battle between self­control and impulsivity  Example #1: Dieting! (Decision to be made: eat the chocolate cake for dessert, or don’t.) ­ Self­control decision: You decide not to eat the chocolate cake, because you know making healthy choices will only benefit your diet results. ­ Impulsive decision: You decide to eat the chocolate cake, because even though your ultimate end goal is weight loss, the immediate reward of that tasty goodness is much more appealing.  Example #2:

Step 2 of 3

Chapter 5.4, Problem 5 is Solved
Step 3 of 3

Textbook: Introduction to Real Analysis
Edition: 3
Author: Robert G. Bartle, Donald R. Sherbert
ISBN: 9780471321484

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Show that if I and g are uniformly continuous on a subset A of R, then I+ g is uniformly