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Unformatted text preview: f ( c ) = c. (4) Let f : X R be a uniformly continuous function and X a metric space. Prove that if ( a n ) is a Cauchy sequence in X, then ( f ( a n )) converges in R . (5) Let f : [ a,b ] R be a continuous function. Prove there exists c ( a,b ) such that f ( c ) = 1 b-a R b a f ( t ) dt. 1...
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- Fall '08