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Define f : Rm \ {0} → R by ƒ(x) = T: Prove that f is uniformly continuous on R" \ B1(0), but not uniformly continuous on Rm \ {0}.

Define f : Rm \ {0} → R by ƒ(x) = T: Prove that f is uniformly continuous on R" \ B1(0), but not uniformly continuous on Rm \ {0}.

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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Only prove the second half of the question 

1 Define f : Rm \ {0} → R by ƒ(x) = EL: Prove that f is uniformly continuous on #4 R" \ B1(0), but not uniformly continuous on Rm \ {0}. ||||
Transcribed Image Text:1 Define f : Rm \ {0} → R by ƒ(x) = EL: Prove that f is uniformly continuous on #4 R" \ B1(0), but not uniformly continuous on Rm \ {0}. ||||
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