Continuity and Uniform Continuity
for x 1;x 2 aas follows. First a2 x 1x 2 since a x 1 and a x 2.Then jx 1 1 x 1 2 j= jx 1 x 2j x 1x 2 jx 1 x 2j a2 (2) where we have used the fact that 11 < if 0 < < . It follows that that the function f(x) is uniformly continuous on any interval (a;1) where
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