For each real function f, define the positive part of f by and the negative part of

Question:

For each real function f, define the positive part of f by

and the negative part of / by

a) Prove that f+(x) > 0, f-(x) > 0, f(x) = f+(x) - f-(x% and |f(x)| = f+(x) + f-(x) all hold for every x ˆŠ Dom (f).
b) Prove that if

exists, then f+{x) †’ L+ and f-(x) †’ L- as x †’ a.

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An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

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Question Posted: Mar 29, 2016 03:57 AM

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For each real function f, define the positive part of f by and the negative part of

Question:

(x)1 + f(x) x e Dom (f.) f+ (x) = ー , r e Dom( し lim f(x)

Step by Step Answer:

a Since fx fx it is clear that f x 0 and f ...View the full answer

An Introduction to Analysis

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