Let M(x) := ln|x| for x 0 and M(0) := 0. Show that M(x) = 1/x

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Let M(x) := ln|x| for x ≠ 0 and M(0) := 0. Show that Mʹ(x) = 1/x for all x ≠ 0. Explain why it does not follow that ∫2-2 (1/x)dx = ln|-2| - ln 2 = 0.
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Introduction to Real Analysis

ISBN: 978-0471433316

4th edition

Authors: Robert G. Bartle, Donald R. Sherbert

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