Homework Questions - Intermediate Calculus | MAT 370, Assignments of Calculus

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MAT 370 — HOMEWORK — SPRING 2000 Homework 10, due Monday, 5/1 Read sections 7.1 — 7.3. Problems: 1. Prove or disprove: if S77) d, converges, then >* | a2, converges. 2. p. 209, # 33. 3. p. 210, # 44. 4. Consider the sequence of functions {f,,}%, given by: er 2 fr(z) = nthe 1) Prove that {f,}32, converges uniformly on [0, 1]. Jn tn=i y (ii) Prove that {f,}%) converges uniformly on [¢,00) for any ¢ > 1. (iii) Prove that {f,}%, does not converge uniformly on (1,900). x 5. Consider the infinite series ys eee, n=0 (i) Prove that the series converges uniformly on [e. .¢) for any ¢ > 0. (i1) Prove that the serics converges pointwise, but not uniformly, on (0,00). 6. p. 233, # 15. Extra Credit Problem 7. p. 210, # dle. The final exam will be held in the usual classroom, LSE-204, on Monday, May 8, 7:40 - 9:30 AM. It will cover the entire course. I will be in my office to answer questions Tuesday through Friday, May 2-5, for several hours each day. I will post a schedule later. You may call to see if 1 am in (965-3286). I am also happy to answer questions by e-mail: [email protected]