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Unformatted text preview: Give the formula and domain of . Let, with , with , with 3 3. Prove that for all , [12] 4 4. (A) State the Least Upper Bound Axiom [5] (B) Give the GLB (if it exists) and the LUB (if it exists) of the set, [10] Explain each with one or two sentences. 5. (A) Let function be defined on , except perhaps at . [5] Give the precise meaning of “ ” . 5 (B) Prove by that . [14] [ Write rough work here. ] Let be given. Choose [ Write proof here. ] 6 6. Compute the following limits. Do not skip steps. You may only use theorems discussed in lecture. Names of theorems are not required. (A) [8] (B) , where is a constant. [8] (C) [8] [ Hint: Do not “substitute” . ] 7 7. Let . (A) Prove . [8] (B) State where is discontinuous. [5] Proof is not required....
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 Fall '09
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 Calculus, Supremum, Order theory, upper bound axiom, Department of Mathematics University of Toronto, Write rough work

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