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Show that r sin (1/x) fails to have a derivative at r = 0 and even the one-sided limits (lim,-0+ (f (x) – f(0))/(x - 0), etc.) fail to exist.

Show that r sin (1/x) fails to have a derivative at r = 0 and even the one-sided limits (lim,-0+ (f (x) – f(0))/(x - 0), etc.) fail to exist.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem Statement:** Show that \( x \sin(1/x) \) fails to have a derivative at \( x = 0 \) and even the one-sided limits \((\lim_{x \to 0^+}(f(x) - f(0))/(x - 0), \text{ etc.})\) fail to exist.
Transcribed Image Text:**Problem Statement:** Show that \( x \sin(1/x) \) fails to have a derivative at \( x = 0 \) and even the one-sided limits \((\lim_{x \to 0^+}(f(x) - f(0))/(x - 0), \text{ etc.})\) fail to exist.
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