Assignment #8 - Due 2.29.12 - MAT 345 Assignment #8 Due...

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MAT 345 – Assignment #8 Due 2/29/12 Please write up your solutions on a separate sheet of paper. 1. Exercise 1 on page 36 of the text. 2. Exercise 2 on page 36 of the text. (You only need to complete (a) and (d).) 3. Exercise 3 on page 36 of the text. (You only need to complete (a), (c), (d), (e), (h), (i), (m), and (n).) In class, we defined a sequence sn converging to s as "for every epsilon greater than 0, there exists a natural number N so that when n>N, the absolute value of sn-s is less than epsilon. We also saw that this definition is equivalent to saying that "for every epsilon neighborhood around s, there is a value N so that the terms of the sequence sn will fall inside the epsilon neighborhood for the values of n>N. We actually drew a picture of this on the board for the sequence sn=1/n^2 and its limit of convergence s=0 and considered the case when epsilon was 1/2. We found that when epsilon was 1/2, then we could let N=1. (That is because the sequence values for n>N would be 1/4, 1/9, 1/16,. .... which would all fall inside the epsilon
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This note was uploaded on 03/20/2012 for the course MATH 345 taught by Professor Michael during the Spring '12 term at University of Massachusetts Boston.

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Assignment #8 - Due 2.29.12 - MAT 345 Assignment #8 Due...

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