|
| | 1a | | * |
| Due 5 September |
|
Please show that the rationals are countably infinite,
i.e., count them. |
| | 1b | | pp. 12-13 |
| Due 10 September |
| # 2a, 3a,c, 4c,d, 7b |
| | | | |
| | | |
| | 2 | | pp. 12-13 |
| Due 17 September |
| # 7d,e, 8e, 9 |
| | | | pp. 29-30 |
| |
| # 1, 3, 4b, 5a,d |
| | | | |
| | | |
| | 3 | | pp. 30-31 |
| Due 24 September |
| # 9, 10, 13, 14 (find only a rational x) |
| | | | p. 61 |
| |
| # 1a,b |
| | | | |
| | | |
| | 4 | | pp. 61-62 |
| Due 1 October |
| # 3, 4, 7, 9, 13 |
| | | | * |
| | | A. Prove that the intersection
of a finite number of open sets Gi is open. |
| | | | * |
| | | B. Give an example
where the countably infinite
union of closed sets is not closed. |
| | | | |
| | | |
| | 5 | | pp. 62-64 |
| Due 8 October |
| # 15, 16a, 17a, 18, 30a |
| | | | |
| | | |
| | 6 | | * |
| Due 29 October |
| A. Please give an example to show why the nesting property fails |
| | | | * |
| |
| for a sequence of nonempty, closed, but unbounded sets in Rn . |
| | | | p. 64 |
| |
| # 26, 29 |
| | | | |
| | | |
| | 7 | | pp. 90-92 |
| Due 5 November |
| # 1b,d, 9a, 10b |
| | | | * |
| |
| Z. (i) Please show that limh -> 0
(cos h - 1)/h = 0 |
| | | | * |
| |
| (ii) Please use the definition of the derivative to find
d/dx(cos x) |
| | | | |
| | | |
| | 8 | | pp. 108-110 |
| Due 12 November |
| # 1a,b, 3a, 4, 6, 14 |
| | | | |
| | | |
| | 9 | | p. 132 |
| Due 19 November |
| # 1, 2, 4 |
| | | | * |
| |
| Q. Suppose |f | is integrable on [a,b] .
Please give a counter example to show |
| | | | * |
| |
|
that this does not imply that f is integrable. |
| | | | |
| | | |
| | 10 | | p. 133 |
| Due 25 November |
| # 8, 9, 11, 12, 15 |
| | | | |
| | | |
| | 11 | | pp. 160-161 |
| Due 5 December |
| # 1, 3 |
| | | | pp. 191 |
| |
| # 3, 4 |
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