exam1_solutions

exam1_solutions - Math 2602 Exam #1 Fall 2008 Name: GTid...

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Unformatted text preview: Math 2602 Exam #1 Fall 2008 Name: GTid (9xxxxxxxx): Instructor: Stephen J. Young There are 4 questions on this exam on 4 pages (not counting this coverpage). 0 Be sure to fully explain your answers, as answers that are not accompanied by explana— tions/ work may receive no credit. 9 Place your name and problem number on each solution sheet. The exams will be separated to be graded. Anyone turning in a solution sheet without a name will receive stern looks and runs the risk of the scores not being accurately totalled. 6 You are to complete this exam completely alone, without the aid of calculators, cellular telephones, personal digital assistants, or any other mechanical or digital calculating device. By signing on the line below, you agree to abide by the Georgia Tech Honor Code, the principles of which are embodied by the Challenge Statement: I commit to uphold the ideals of honor and integrity by refusing to betray the trust bestowed upon me as a member of the Georgia Tech community. Student signature: III-- Math 2602 Exam #1 18 September 2008 1. (5 points) Count the number of ways to arrange the subsets of {1,2,3} so that no subset appears before all of its subsets have appeared. For instance, for the set {1, 2} there are two such arrangements: 0, {1} , {2} , {17 2} (0, {2} , {1} 7 {17 2} For the set {1, 2, 3} one example is 0, {1} a {2} 7 {17 2} , {3} a {2, 3} , {1, 3} , {1127 3}~ D0 an a {93%}, wk 4“ 5 wslwc 136,16“; {1,2333 Wholesale-13f: 52%; us tuna we as lax; z a» an! £141 a 4m— 2 4,1450%, as a gen Mat 2 w about 3K 2 51/er IA {5m 2 7%?“ (1‘3 95', :42, m, 2111,24,, fad/gas , all”; Mendez ‘1 2w. Z25 Ze— wga; 2w- gates (73 52’ t , 1 $1. Mw \QK mg) @2915], (I; 72 ,QA/maa/yk 75% We; (a we flange/vag/éeawé foe v fefi , I W HQ: 74M0 544, so VKV‘WC ($10136) aqué, {747744, i’lOWé‘LKQpW 25 3754712978, Page 1 of 4 Name: Points earned: MNMWWM mmmWWWMWmwMWw"WW.m.mwwmmmwmwmmww.vm. ma 'rwnwnm Math 2602 Exam #1 18 September 2008 2. (5 points) Prove that for all real 2: Z —-1 and integers n 2 1, that (1 + x)” Z 1 + an. Cowstflw’ l4=\) [+X2/1LXE SW“ 4/ “‘76‘2 (“JMMVW /-47~‘4-k X\+ 9— } + >09. mm We“, (MW: (m (w (l+><\ (15% LA 2 32m (lip-)6 ’2 C). 3’ 3~H¢><+X+k><z *3 I+(L+\\X‘+LLX% Maw HM]; Mac/le QM ox,“ X2 ~l M23 m (lHCY/LZ [1‘- {A Page 2 of 4 Name: x2920, éé [L320 M V463 [MW/M 1*an a /+ (LL/3X; 2 ml) Points earned: Math 2602 Exam #1 18 September 2008 3. (5 points) Suppose a0 = 5, a1 = 0, a2 = 30 and a3 = 30 satisfy the recurrence an 2 ban_1 + can_2 for n 2 2, where b and c are fixed constants. Find b and c and then find an. “Wm 30: w +05" mm. we w) 30-:5'3o~+a~c> we tar-L Page 3 of 4 Name: Points earned: Math 2602 Exam #1 18 September 2008 4. (5 points) Use an appropriate sorting algorithm to order the following functions by their asymp— totic behavior: ____ 2 10g3(4n2 + M”) = 3R2 - 2n + 1 mm = 4M + (~2>"+4 hm) =10gw) f6(n) = '1‘ TL 3»; “ZlM‘l . “Z q k?) zmfil 1 mm gf-A 4) n, 414$: is; WV” 3" ‘27 Page 4 of 4 Name:____________ Points earned: $04 $114 {4 «£3 4 $2.4 "95’ WWW“Wm.W‘mt«WW:mwmwwmmwmwwwme.nammwmwmmuewnwamm iséiégéfix re??? ...
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exam1_solutions - Math 2602 Exam #1 Fall 2008 Name: GTid...

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