MATH 211 Exam 1, Spring 2008

AMERICAN UNIVERSITY OF BEIRUT Math 211- Spring 2007 Drop Quiz 10, section 1, May 17, 2007 Names oo. o eee e eee ee cee ee ence eee enees AUB ID number: oo... eee Section: ....... Question I: : (1 -powit) How many subsets of a set of n elements contain more than one element? : Num ber of su kee ts comtetatina O «2hearerts - AL Za ve ao DS 4 etemont: mn Ve tex { none ber off Subsets Q” A, nem an haw our els rl | a Num eer Of Sulesed \ be 2 ere —_ Question 2: 7 (L:Spoints) How many positive integers peel 100'and 999 inclusive: ——> There ace 200 nhe wm Hed Maule a) Have distinct digits? x4 x8 b} Do not contain the same digit three times? 4, A0~ ~ 4 = $41 c) Begin with an odd digit? Sy ‘Oo d) Are divisible by 9? Abo ¢ AR < BAA ,;.-180 = RR \ Mn a Sh 5 here are A00 such Ws BR Sih umn leet Question 3: nel poifits) Let a, = 2(-4)" +3, for n=0,1,2, Is the sequence } a, } solution of the recurrence Fe lation a, =—3a,_, +4a,_.? a “2 ~sa 44a, = -3facu “43 44 Ca cop tee) = 66-4 GA ECO LID = 64 4s 3 (-4" Cuy*Loe] #3 = A(-4y 43 , : = Aa a6 Ayn AL bet or - Question 4: iz pret ) (2.5:-points) a) Find the solution to a, =a,_, with ag =1, a, =2 , a, =3and a, =4. - ; ~ (use *k of th j use back of the page} a,= 4 _ 4 (aye 7 cos (n E) ah (>) b) What is the general form of the particular solution o the linear nonhomogeneous recurrence relation a, = 4,4+n(3)"? First aves a? = = (Em +F\3" (oe du 7 ca bien) Alcan ted c) What is the general form of the particular solution of the linear nonhomogeneous recurrence relation a, =a,.,+7 (-1)" 2 First yess | Q® - ae Fr + G) (- vw : A » Te da $e’ GZ, one te Ton aN a (nee Rust ow a) Comecled guess: a? = m(En4 fat 6) (-" a,of, oa3z 7 a — Agha ow “f Ct\ (e) % reluhou of _4t=0 C Cy Charactens KO eauabon. (t- N Gere Cx? eh) =o Yet , Y=-t ; “a= Ae Tyan 4 L 7 { aS We emo Kot eon 4 > ht Az é _ . Bo e = Vor §? 24 ~ AL OW 625 C<enctal pallor of UN" Ni a,> A + Bey -_ Cees(oE\ + Dam os) Pour ajet AD ( a tHe CO _ 4 (ay eee & B&B adD=Aa ( a2>% A +R8-C =9 te | ois A _& hy 2d (43 (a) -@) aives aC =e QD Ce-h Ue) _ YS n 2d = 2 hot Peeshtle in @) AYR =D (by ABR 23