x3-day1a - Exam 321. Name: @\ Ml 75—001 (1 pt.) Iran,...

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Unformatted text preview: Exam 321. Name: @\ Ml 75—001 (1 pt.) Iran, 2009 1. (10 pts.) Consider the sequence _ n+3_ I _2n—1’ '— an (a) Graph the first; six terms of the sequence on the axes provided below. Be sure that your axes are properly labeled. 3 H i i é (b) ComputeI1i111_e...n. (90 z I" ) at: l 3Q; ' 3 ) a; S n—>.’x.- ‘ 51. 6] 2. (25 pts.) Determine if each of the following is convergent or divergent. CIRCLE YOUR, ANSWER. You do not need to Show work= but you earmot. receive partial credit for a wrong answer unless I can see how you got your answer. / "xxx 00 n. — 1 _ . a — DIVERGENT ( ) Z .a'nfi + 2.” n=2 a... INVERGENTE 00 n2 + 2111 n T .1 (m 2:75jifif— CONVhRGle INVERGENT m 2 4 /xrr’ff::r~\ I n + _ 'H. l _‘ 1 (d)§: T6” CONVERGhNT (:HinyReENfraem> 'n=0 -—-_._._____.H_._-—-—-r/ ,F _ _ DIVERGENT . T (a 2:35 CONVERGENT 2. (25 pts.) Determine if each of the following is convergent or divergent. CIRCLE YOUR ANSWER. You do not need 1.0 show work: but you cannot receive partial credit for a wrong answer unless I can see how you got your answer. DIVERGENT w n2 —|— 211110. 1 r 1 (b) 2 CONVERGle DIVERGENT °° 271+ 4'” f’ __'_“_r_::\ (d) 2 Mn CONVERGENT DIVERGENT we n.=0 " I (e) 4 CONVERGENT DIVERGENT n=0 3. (5 pts.) 011 the previous page there is exactly one geometric series. (a) Which one is it? ( CB (b) If it converges, compute the exact sum of the series. if it diverges, explain why. 5 2(2)“ H 4. (10 pts.) Find the radius of convergence of Z ILL—ii; 2n-i-1 n=2 2 fl " I n t I an ' T n ' “ fl -" 2 “.1 (3X1-Z) Z 3x+2 _ \ ¢ < i 2 “2 < 3¥+ Z 5 Z .. Li c EA (— 0 ~ 11/3 c x( O 455/- O r 3 . v __ _ a. A 2. (cam/Led: “2/3 J AJVOJ' 3 5. (10 pts.) Express fix) 2 3 2 as a power series centered at U. — :1: = i _|_z—— : Zi[l+ EX’“ (-%“3'T< 3 1— Ex 3 III J '. Z L “i 3 S5 R __ —-—-—~ '~#— -1'- __‘X “" WK +- * 3 x “L 61 A 2.7 SH {5. (10 p135.) Find the quadratic approximation for = (1 + 11:)U3 centered at U. M a ‘- M 1+ ( 1 Ex + (2.\)\ 3: l _k_ + (3 xi 2: l J— }.m L_ I I —+' ,3 X _ a X I 7. (10 pts.) Find the fifth order approximation of cenLOI‘ed at 0, given that = 2 and the derivative of f is ,Hzcosa; f0») 1+3? JZIA. ’(m .. (/fll 2 i a ({- 1+ 9 N {+Ki: -‘ 5x +2q)‘ X X. Z - l— A ’r 2H t K - 1x2 + lax ~ ixé _L ~+ I 6 l_ .9 +291)“ * 31X flax / 3 z '1 LK3 +1 37»; 1C 1: 6* x# Z {20 ...
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x3-day1a - Exam 321. Name: @\ Ml 75—001 (1 pt.) Iran,...

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