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Unformatted text preview: n 2 n + 1 n 2 + n 2 n-1 n 2-n = lim n 2 n + 1 2 n-1 n 2-n n 2 + n = 1 since the leading term on top and bottom is now 2 n 3 . (7) This limit will be 0. If we apply LHopitals Rule repeatedly we end up with 18 24 n which goes to 0 as n goes to innity. (8) This limit exists and equals-1. (Recall arctan n goes to / 2 as n goes to innity.) (9) Since (1 + 1 /n ) n goes to e as n goes to innity, this will go to e 2 . (10) (a) The numerator goes to e and the denominator goes to . So the quotient will go to 0 as n goes to . (b) An form so use LH opitals Rule to show that the limit is 1 / 2. 1...
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- Fall '07
- Geometric Series