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Unformatted text preview: MATH 242 Analysis 1 (Fall, 2011) REVISED Assignment 2. Due in class Tuesday, 4 October.- Questions 3b and 8 have been slightly re-worded. Instructions: This assignment is out of 50 points. You may choose any questions whose points add up to 50. As in the previous assignment, provide all details in your work. Also as previously, stars (*) indicate possibly more challenging questions. 1. (10 pts.) Using the definition of the limit of a sequence prove that (a) lim 3 n 2- 1 2 n 2 +5 = 3 2 , (b) (cos(3 nπ/ 2)) is divergent. 2. (10 pts.) Prove or disprove (a) If [For all n ∈ N , x n < 2] then [ lim x n < 2 or the limit does not exist], (b) If lim x n < 2 then there exist M ∈ N and c > 0 such that for all n ≥ M , x n ≤ 2- c . (By convention an assertion such as “lim x n < 2” contains the assertion that ( x n ) is convergent.) 3. (10 pts.) [Your work in (b) should not assume results from calculus; assume only the definition of e as given in 3.3.6 of the text, as the limit of the sequence ((1 + 1...
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This note was uploaded on 03/25/2012 for the course MATH 242 taught by Professor Drury during the Spring '08 term at McGill.
- Spring '08