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eHomework06 - eHomework 6 Directions Determine the answers...

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e Homework 6 Directions: Determine the answers to the questions below. Then open the EMCF eHomework06 on CourseWare ( http://www.casa.uh.edu ) and submit your answers no later than Friday, February 26 th at 11:59pm. 1. Every Cauchy sequence converges. a. True b. False 2. Every monotone sequence converges. a. True b. False 3. Every bounded monotone sequence is a Cauchy sequence. a. True b. False 4. The LUB of a bounded decreasing sequence is the limit of the sequence. a. True b. False 5. The LUB of a bounded increasing sequence is the limit of the sequence. a. True b. False 6. The GLB of a bounded decreasing sequence is the limit of the sequence. a. True b. False 7. The GLB of a bounded increasing sequence is the limit of the sequence. a. True b. False 8. Every convergent sequence is bounded. 9. A convergent sequence can have a subsequence that diverges.
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10. A convergent sequence can have 2 different subsequences that converge to 2 different values. a. True b. False 11. The sequence ( ) ( ) 1 n has only 2 convergent subsequences. 12. According to the lecture on 02/22, if
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