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Unformatted text preview: be a continuous function and assume that f ± ( x ) exists everywhere. Assume also that there is a constant α < 1 such that, for any x ∈ R ,  f ± ( x )  ≤ α < 1 . Prove that f has a unique ﬁxed point. [ Hint : use problem 7 from Homework 6.] (c) (5pts) Suppose we only know that  f ± ( x )  < 1 for all x . Does the conclusion of part (b) still hold? [ Hint : think of slant asymptotes.] 3. (10 pts) Problem # 2 page 114 in Rudin . 4. (20 pts) Problem # 13, parts a), b), c), and d), page 115 in Rudin . 5. (15 pts) Problem # 6 page 114 in Rudin . 6. (10 pts) Problem # 7 page 114 in Rudin . 7. (10 pts) Problem # 26 page 119 in Rudin ....
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This note was uploaded on 12/07/2011 for the course MATH 18.100B taught by Professor Prof.katrinwehrheim during the Fall '10 term at MIT.
 Fall '10
 Prof.KatrinWehrheim

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