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# Mathematical Thinking: Problem-Solving and Proofs (2nd Edition)

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Homework 17 - MATH 310 0101 - Summer I 2010 - Due by Thursday, July 8 1. Exercise 14.1 2. Exercise 14.2 3. Exercise 14.29 4. Deﬁne f : R R by f ( x ) = ± - 1 if x < 0 , 1 if x 0 . Show that f is not continuous at 0. Do this in two ways: (a) Use the “ ± - δ ” deﬁnition. (b) Use a sequence. 5. Exercise 15.4 6. Exercise 15.7 7. Exercise 15.8 8. Exercise 15.11 (One way is to modify the proof of the Intermediate
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Unformatted text preview: Value Theorem. There is a much easier way.) 9. Exercise 15.12 10. Exercise 15.13 11. Exercise 15.16 12. Exercise 15.19 (A function satisfying the condition in the exercise is called a Lipschitz function.) 13. Exercise 15.21...
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