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Download Homework Problems - Advanced Calculus I - Spring 2000 | MAT 371 and more Assignments Advanced Calculus in PDF only on Docsity!
MAT 371 — HOMEWORK — SPRING 2000 Homework 5, due Friday, 3/3 Read sections 4.1 - 4.4 (skip Theorem 4.11 and the Lemma preceding it, on page 125). Problems: 1. Prove that x is uniformly continuous on [0, 90). 2. Prove that sin(«?) is not uniformly continuous on R. 3. Let f,g: DR be uniformly continuous, and assume that D is a bounded set. Prove that fg is uniformly continuous on D. 4. Let h: EB > R be uniformly continuous. Suppose that {z,}2_, is a Cauchy sequence in E. Prove that {h(z,)}%, is a Cauchy sequence. 5. p. 106, # 44. 6. p. 106, # 46. Extra Credit Problems 7. Prove by ex ample that, in general, the product of uniformly contimious functions need not be uniformly continuous, even if one of the fictions is assumed to be bounded. 8. p. 106, # 48. Test 20 Friday, 3/24 Math Department Testing Center Test 2 will cover chapters 2, 3. and 4. Your review should include definitions. examples. statements of theorems, and homework problems. You should also be able to supply proofs for the casicr lemmas and theorems in the text. (+ * +) NOTE FRIDAY HOURS OF THE TESTING CENTER (« + «) You may take the test during any 2 hour period between 8:00 am and 5:00 pm. (No exams are given out after 3:30 pm.) You must bring your ASU SUN ID, and the preprinted label that you will receive in class. Books, notes and calculators are not allowed. You must keep track of the time so that you do not take more than the allotted 2 hours. More information about the testing center is available at their webs http://fym.la.asu.cdu/ fyrn/TestingCenter /ts Homework 6, due Friday, 3/10 Read sections 5.1 (Example 5.4 is optional), 5.2, 5.3. Problems: p. 129, #5. p. 129, #7 (prove your answers). p. 130, # 8. . 130, # 21. p. 131, # 2¢ p. 131, # 25 (prove your answers). Credit Problem . p. 131, # 27. Soe Rep Extr: > 
