(a) Prove that f+(x) ~ 0, f-(x) ~ 0, f(x) = f+(x) - f-(x), and If(x)1 =...

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(a) Prove that f+(x) ~ 0, f-(x) ~ 0, f(x) = f+(x) - f-(x), and If(x)1 =

f+(x) + f-(x) hold for all x E Dom (f). (Compare with Exercise 1, p. 11.)

(b) Prove that if L = lim f(x)

x-->a exists, then f+ (x) ---; L + and

f- (x) ---; L - as x ---; a.

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An Introduction To Analysis

ISBN: 9780131453333

3rd Edition

Authors: William R. Wade

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Question Posted: Jul 20, 2024 05:01 AM

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(a) Prove that f+(x) ~ 0, f-(x) ~ 0, f(x) = f+(x) - f-(x), and If(x)1 =...

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An Introduction To Analysis

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