# Proof: Uniformly Continuous

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The following theorem could be used to write the proof.

A theorem states that if d:D-->R is uniformly continuous on D iff the following

condition is satisfied:

If un and vn are both sequences in D, then

lim as n-->infinity (f(un)-f(vn))=0

Show f is not uniformly continuous on D making use of the sequential characterization of uniform continuity.

f(x)=1/(x^2-4), D=(2,4]

hint:Considering sequences that converge to 2

f(x)=1/sqt(x) , D=(0,3]

hint:Considering sequences that converge to 0

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##### Solution Summary

How to prove a function is not uniformly continuous is determined. The sequential characterization of uniform continuity is examined.

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Please see the attached file.

Consider the first function , D = (2,4]. To prove that the this function is not uniformly continuous, it is enough to ...

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