Assignment 6

# Assignment 6 - a n for n ≥ 1 Determine whether a n...

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Math 138 Assignment 6 Fall 2008 The following questions are to be answered neatly and completely on standard size (8.5 by 11 inch, or metric equivalent) paper. Please insure that your name and ID number are clearly indicated on each page, and that all your pages are securely fastened together, staples are preferred. This assignment is due at 9:00 a.m. on Friday, October 31, 2008 . 1. a) Use the ± - δ deﬁnition of lim x a f ( x ) = L to prove the limit: lim x →- 5 ± 4 - 3 x 5 ² = 7 . b) The deﬁnition for the limit of f ( x ) as x tends to inﬁnity is: lim x →∞ f ( x ) = b means that for all ± > 0 there exists R > 0 such that for all x , if x > R then | f ( x ) - b | < ± . Use this deﬁnition to prove that lim x →∞ x 2 + x + 1 x 2 + 1 = 1. 2. Determine the limit of each of the following sequences, if it exists: a) ³ ( - 3) n 2 2 n +1 ´ b) ³ 2 2 n n ! ´ c) µ 4 n 2 + 3 n - n 3. Let a 1 = 2 , a n +1 = 2 +
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Unformatted text preview: a n for n ≥ 1. Determine whether { a n } converges, and if it does determine the limit. 4. Find the sum of each of the following series, if the sum exists. a) ∞ X n =1 2 n +1-1 3 n b) ∞ X n =2 4 1-n 3 n-1 c) ∞ X n =1 3 n 2 + 3 n 5. Determine all values of x for which the following series converge. a) ∞ X n =0 · x 3 ¸ n b) ∞ X n =0 ± x-2 √ 5 ² n Please note that assignments may be submitted to the drop box before the due date. Assignments will be removed from the drop box shortly after the time they are due. The drop boxes are located on the fourth ﬂoor of the Math and Computer building (MC) outside room MC 4066. Check the course outline for the box/slot for your assignment....
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