Unformatted text preview: F = f ◦ g is continuous at x . 5. Let D = IR \ { } and f : D 7→ IR be deﬁned by f ( x ) = 1 x . a. Is f continuous? Prove that your answer is correct! b. Is f uniformly continuous? Prove that your answer is correct! ( In either part you may use any theorem proved in class or in the homework ). 6. Let Q be the set of rational numbers and let f : Q 7→ IR be deﬁned by f ( x ) = 1 q if x = p q with p,q ∈ ZZ, q > 0 and gcd( p,q ) = 1. For each of x 1 = 2 3 and x 2 = √ 2 either prove that lim x→ x i f ( x ) does not exist, or calculate the limit and prove that it is indeed the limit....
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 Spring '07
 thieme
 Calculus, Metric space, Cauchy sequence, Calculus Midterm exam

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