This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 Wholesale13f:
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~‘4k 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 tarL 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 gfA 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??? ...
View
Full Document
 Spring '09
 COSTELLO
 Math

Click to edit the document details