MATH 355 Final: MATH 355 Amherst F16M355Final
15 Feb 2019
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Read this first: please turn in your four take-home final problems (7. 2. 5, 7. 4. 5, 7. 4. 6 and 7. 5. 8) now . Please make sure your names are on the sheets you"re turning in: this is a closed-book examination. No books, notes, calculators, cell phones, communication devices of any sort, webpages, or other aids are permitted: please read each question carefully. Show all work clearly in the space provided. Grading - point values of each problem indicated. Suppose that {an} is a decreasing sequence in r; i. e. , an an+1 for all n 1. Show that if lim an = 0, then an 0 for all n 1. n . Suppose {xn} and {yn} are cauchy sequences in r. (a) show the sequence of sums {xn + yn} is a cauchy sequence. [15] (b) show that the sequence of products {xnyn} is a cauchy sequence. The intermediate value theorem (a) state the intermediate value theorem.
