Mathematics Homework Solutions
#84783
Proving that f is not uniformly continuous
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
How to prove a function is not uniformly continuous.
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