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 sns 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
neighborhood of 0 of 1/2 to 1/2.) Now what (a), (b) and (c) are doing is asking you to consider
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 Spring '12
 Michael
 Sociology, Elementary mathematics, EPSILON

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