{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Exam 01 - Math 2602 TESTl Name gem/UK Problems(P1(10 pts...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 2602 TESTl Name: gem/UK. Problems (P1)(10 pts) 1 (P2)(10 pts) I (P3)(10 pts) (P4)( 10 pts) [Total H Scores ’ TIME ALLOWED: 50 MIN SHOW YOUR REASONING TO RECEIVE CREDITS Problem#1.Decide which of the following Claims are true. Write True or False and Justify your answers. (a) 4n? + 12 : 0(2n3 _ 1) ‘1 E5 ‘. TWE , w _ L}{\1+lz , 1 .. 3" =5 Lln’L-HZ :0 2 }_‘ 3mg 2/3“!“ 933394 = 0 I Lm +\2 - 004» 3 > (n Yr)“, (b) 27;): 0(n2) NO \ VASE, J33“ Elizw m» n ”(find :2; “3:09-33 Yl~>m VxL ‘ ‘5 2n3+0(“1\ (C) 2103< 3<)=o32)n WES‘ Tm: [\M 292030)} . : ltm ’13.: z.- 0 :_>> -l\03(n3) = 9(3VCL) W600 3%“ “am 3 1“ \ 3, . (d) 2103032): 3310332)) N° 2 2:2 Me ————2»-‘““ 2,2“ -333 W333)! (333)) “~59“ 310 2 m t (e) M + 8log(n9) + 4 = @(3n6 — 2) 7g§l 33333; (23 23‘233933 (3“) +1) .. :32. #0 :> 23% xhgh‘llw = @:%é~1l W505 ant a ‘2 Problem#2. (a) (5 points) Find the formula for _ j i 2 I n a”_Z(j+1)!*2!+3!+ +(n+1)!' i“ i”‘*‘ 2 > (RE: ‘ :” <7, “ 1-“ 53‘ {3‘ (9*\)\. 4“: 3 (3H) \ (\ . 3 _ K A- _._._. (b) ( 5 points) Prove your answer in part (a) by using induction. R 4. M4 _ ‘ 3,.) am: A— 1— :kwwl. LHS-(\‘H)\ : 21-2 ) , 1\ :1 2 LHS 2W5 \/ k ‘ \ 2.. : I- ’— was Jmn éz Lamp,“ 2 3W M 266)! GM» 5:! A+l 5 A , '1’ A M W. 6;; 477 k: m . 67m 7 " (WM, w“ 174 “’7‘ M-H * a U .L 32+: + 1‘; + —-——- 6:3 _, 2M + 3‘? 51‘“)! (mm ’3“ W 3 \ A Wt“ (Wm) (mt): _ wt mm ~ ._ ‘ .1. M (mat) 3 (“—616 §\ 5 ‘ (may! Problem#3. (a) (4 points) Calculate gcd(138,36) by using [Euler Algorithm. (’0 , \38 == $936+" 30 3% / S'G ‘Q’O‘ , -' (3) (b) {3 points) Use part (a) to find integers k and m such that 138k + 36m = gcd(138, 36). Cm ==> ‘4 r 34’ "‘ 30 :> (:96— (mr— 2130 .335 (43 ::> z 30 =9 ‘36 6:- 4.34438 30 \L2" ) mthf (C) {3 points) Use part (b) to find the general solution of 23x"+ 6y = 1. WW) 1> 6: we» ~88 :5 «= Lt'é‘l' 23.90 WWI/{A ’ 0 Wk ) SmM1W‘3. 3: 304.33“ ‘3 Lf‘tQZV‘ 4 Problem#4. (a) (3 points) In a certain computer system, a file name must be a string of letters and oligits7 1 to 10 symbols long. The first and last symbols must be numbers and the computer makes no distinction between uppercase and lowercase letters in any position. Thus 1amkA4 and 1AM ka4 are both the same legitimate name, whereas a1mkA4 is not legitimate. How many legitimate file names are there 7 Express your answer as simple as possible. /\ 9);“on 1P“) 1 1.0 garter A3 ' mmfl Wrrww‘ 3 WQ '. lOX’HXlO . H 9%:on 15% .1 \oxzéxZéxlo .. M0 w 3 Q a w 36x34 x 53M 1 W L} 3’ W5 \0+ \Ozt 36 \o"+ , 36" \o"+ -- a 363 lo =|0+l0 (b) ( 5 pomts) How many integers from 1 to 2007 are divisible by 3 or 5 or 7 ? Lilongwe? 6651f] LEM—ii: 40‘ L:m9—J= Q86 \Efiiaw Lam? :75 L391”; :10] :ttgrlmkjm {heat} 0/ 5 or a» is 66%er +234- tar—WMS +I‘i 2* mo ‘ (o) (2 points) How many integers from 1 to 2007 are not divisible by 3, 5 or 7 ? 1:} ”#55515 m ”A” Jim/MEL. L2, 3; § or 3‘ ——~ 0300?... [030 ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern