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Show that the following functions are continuous but not uniformly continuous on their domains: (a) f: R → R defined by f(x) = x²; (b) f(0, 1)→ R defined by f(x) = 1/x; (c) f (0, 1)→ R defined by f(x) = sin(1/x). .

Show that the following functions are continuous but not uniformly continuous on their domains: (a) f: R → R defined by f(x) = x²; (b) f(0, 1)→ R defined by f(x) = 1/x; (c) f (0, 1)→ R defined by f(x) = sin(1/x). .

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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[Ex8 Q3] Calculus question about continuity :)

3. Show that the following functions are continuous but not uniformly continuous on their domains: (a) f: R → R defined by f(x) = x²; (b) ƒ : (0, 1) → R defined by ƒ(x) = 1/x; (c) f: (0,1)→ R defined by f(x) = sin(1/x).
Transcribed Image Text:3. Show that the following functions are continuous but not uniformly continuous on their domains: (a) f: R → R defined by f(x) = x²; (b) ƒ : (0, 1) → R defined by ƒ(x) = 1/x; (c) f: (0,1)→ R defined by f(x) = sin(1/x).
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