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Unformatted text preview: 1. (12 points) For each sequence below either calculate the limit or write does not converge: a. lim n- > n 3 (2 n- 1) 3 ANS: This converges to 1 8 as this is the ratio of the coefficients of the leading terms and the polynomials have the same degree. b. lim n- > ne- 3 n ANS: This converges to 0. We can think of e- 3 n as either exponential decay, or as an exponential function on the bottom of a fraction. c. lim n- > (- 1) n + 1 n ANS: The first term (- 1) n oscillates, and the second term goes to zero, so their sum doesnt converge. d. lim n- > sin( (- 1) n n ) ANS: This converges to 0. To do this one you had to remember that: lim n- > sin( (- 1) n n ) = sin(lim n- > (- 1) n n ) because sin is continuous. lim n- > (- 1) n n = 0 . sin(0) = 0 . 1 2. (14 points) Place each sequence in the appropriate place on the following list by either putting the sequence in the same box as a sequence that has the same rate of growth putting a sequence between two boxes, to say that its rate of growth is slower...
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