Mat 243 review exam2 sols(2)

# Mat 243 review exam2 sols(2) - MAT 243 REVIEW EXAM 2(1 Fill...

• Test Prep
• ZippingAce3
• 5
• 92% (13) 12 out of 13 people found this document helpful

This preview shows page 1 - 5 out of 5 pages.

#### You've reached the end of your free preview.

Want to read all 5 pages?

Unformatted text preview: MAT 243 REVIEW EXAM 2 (1) Fill in the blank in the statements below: (a) A function f : A —&gt; B is one-twone if and only if V5.11, e A g chl ) = 9’04») &quot;—2)&quot; = Kb) (13) A function f : A —} B is not one-to—one if and only if 3 3%: 6A ( E: liki) A XI :f Xe) (c) A function f : A —&gt; B is onto if and only if Vﬁe C) EKG/H 2-55 J =13.) (d) A function f : A —&gt; B is not onto if and only if 2%6 biXéﬂi 2&amp;23 ‘3) (m) A sequence is a function whose domain f§ ill 541' CL Viola-N (144': 'Ue “Juana ﬂame“. 2 (n) An arithmetic sequence is a CAM whoee domain {'5 H: 5!} 09— Vick - W 6. rm. CHE (3145. (o) A geometric sequence is a in LX &amp; 2‘11? &quot;0 hfﬁabwhose domain {3 gﬂ SJ‘OE Mom —M\$344.‘oe (2) Prove that f : Z —) 2; f (n) = 3n — 5 is one-to—one but not onto. Ch“ 9%- . aha-lo ”om ' Assm 3n, —S= 3% &quot;5* Wm n, “if. m ##- QILQA'PIAMa. 84903115. 77”» 3&quot;: :— 3“; ”I in; ' 'i N0; Ohb' 0G)&quot; [a ‘5‘ TM ('5' 140 (“pail “1&amp;9“, Pb Sud: +4.2! . I.&quot; (t £Ck):3n—S=S. TL: 043 §aMxxA rs. 1% win» 5 he; 5“&quot; ‘chl‘g'l, l (3) Prove that g : R —&gt; HP U {0}; 9(1) = (33 + 3)2 is not one—to-one but it is onto. Mo+m-fom. gun-Jo Md are. TM» .- 1: : &quot;' GP X7131 (gay—('5).— Cale) of G) a“ 015%; 2 m 243 REVIEW ms 2 {4) Letf : IR —&gt; R; f(:r;) = 12. (a) Find m—s, 2)): E0: ‘11 (b) Find f-luo, 1)) = H 0) W&quot;! ') (5) Letf : R —&gt; R; ﬁx) = sins: (21.) Find m—gm); 5%,?) (b) Find r1({0.5}):§ JE+ 192&quot;} £41— + @217] W“ lg M a ma {Kleqmi (6) Let} = 1R: a Ha; Ha“) = li—EJ- (a) Find m—Lm): 2-0 0,5 3% (b) Find f—l{{15}) .2 [80' 953 [Q 4 3!. a. :1 g as x 4 95 (7) Evaluate the sum and simplify as much as possible Show all your work. Calculator an— swers will not be accepted. 30 = Zii2(k+3)2- 2 (2+3) — 2 CM)&quot; (2.0%) ‘G l2: I '2&quot; 2*: (:296+62k+2300_ IQ- 3g3|£+y323l+210l6 k-l 2&quot; 2-1 (““155 + 2.qu +210 #16 - ‘l (8) Evaluate the sum and simplify as much as possible. Show all your work. Calculator an— ‘21—”? swers will not be accepted? ’2' Z. 2{:+1) Z s. i L': = 2&quot; ( ) k ‘15' '2’; I: has '2 ‘ .9— __ 21(2 G'g’l'jé)):2[(\$)w l—l—g: . i=0 25¢ _?_ -l (9) Find the sum. Show all your work. Calculator answers will not be accepted. I! C (—6)+(—2)+2+6+10+...+442 &quot;’ £3: 2 (‘3') I __‘l 2—6442&quot;! = ”1‘7“&quot; 5‘ '3 I2=O In. :05) + ‘12 (ans 4— ﬁlﬁ’lf “3 (—eDII'erz :12, us =2‘t03‘r MAT 1243 REVIEW EXAM 2 3 (10) Find a recursive deﬁnition for the following seuences deﬁned 1) the closed formulas: (a) a&quot; = —3 — 5n. 5 a. nun l (4. so 6...} c‘k-I [ EEK-1M (b) an = (—5)-3“ -‘ J «r a «Au—ﬂew h BEE! (11) Fill in the blank statement below. (a) A function f3&quot;) isﬁ’i'g-O {if 9(1) if and orily if L141 (Xi-54 (0145th C. and [’2 suck“. it) .40 late&quot; at x». (b) A function ﬁx) is big-Q of 9(1‘) if and only if 1124!. “(3&quot; CMMS C “ilk SucL M 10—69??— claim) vP—XHa. (c) A function f(:.-:) is big-6 of g(:c) if and onl_ if {.0065 0038:) we! (109:2. 0:). (c) Mien f(;r) is big-9 of 9(1') then we say that ﬁx) and 9(3) are of “PL! Saw Odd—n (12) Use the deﬁnition of &quot;f(:r) is O(g(r))&quot; to Show that ﬂat) = 4534 + 2513 — 3(log(x))4 — 821:2 — 781' + 10023 is C(34). Find witnesses C and is so that |45.1:&quot; + 251?2 — 3(log(:1:))4 — 82:11&quot;.2 — 782: + 10023| S C - |:r“] whenx&gt;k. 4 x 4 K \ H§x*t1g{1+éxb8x)?) +6ng1) +C-‘1L80i- [0023‘ .. ﬁx)! LISVHIJJS'VE’I 4- 3\’(&quot;I+811KLI “WM HX‘? é: Ioozsex‘ aim/1mm Luz“! m M 449le +lx“( '-= ”L x” 23¢: 1/] 6:2“ ,2 =11 w ct»: Choose a function 9(3) as simple as possible no u e 5m. est order such 1'. at 0(9(I)) x 'f __ . _ 4— m + '3‘ “( lq x! '3 j O( 3 ' p to. --‘t 3 3) ‘4 00“) =- ._ ,( 92.1»2 (2) V&quot; “(2'1&quot; MAT 243 REVLEW' EXAM 2 3 (10) Find a recursive deﬁnition for the following sequences deﬁned by the closed formulas: (a)an=-—3—5n ell-g.) 0.292;:77—3/ m .51 (11) Fill in the blank statement below. (a) A function f (1:) is big-0 of g(;r:) if and only if (b) A function f(z) is big-Q of g(:c) if and only if (c) A function f(:i:) is big-9 of 9(35) if and only if (c) When f (1:) is big-8 of 9(3) then we say that f(:::) and g(.L') are of (12) Use the deﬁnition of ” f (I) is O(g(:c))” to show that ﬁx) = 453:&quot; + 25352 — 3(log(z))‘i — 32172 — 781? + 10023 is 0(1“). Find witnesses C and I: so that |45\$4 + 251-2 — 3(log(:c))&quot; — 82st:2 — 78:: + 10023| 5 C&quot; II‘I when 3: &gt; k. (13) Give a big 0 mtimate of ﬁx) = (21+91nx+5-3\$)-(m2+91nx—9x3)+(—9x+5-2I+2x?)-(2+3—1.0001=41m). Choose a function 9(3) as simple as possible with the smallest order such that f(:c) = 081(1)) . 3 ﬂ ' x ‘1- _ ' olx_ EMA&quot; (Zx+qﬂn¥+s-s‘)- (WWW! “W (W l 1’ 3 N x ~ c. 1 Loan 3. Moszlhx13J= O( wool&quot;) 10({5 @W W 0( 2810001”) 3 00-0092: 4 MAT 243 REVIEW' EXAM 2 (14) Give a big-O estimate of the number of operations, where an operation is an addition or a multiplication used in the segment of the algorithm below ‘ . at! 16°F tz=0 dimer-Io) 003951,”; We. on ms: 9‘ __ L fol-i;=10ton2+3né’ (h) Tine-5} l°°l° has 0(2 4-51.. 2. )&quot; for} := 2&quot; to 2&quot;+5n p 0 ‘ I 'MaJ'I‘G“: Each r'l-I’LJ-ws 00'») E 13==t+ij &lt;5— ladd-‘m‘ 'M at) 0(h)‘ k on) oP‘chmHs. ““5 endfor CM ‘6“): GUM-F‘Q‘} end fer ‘HJ- S'LOOP WP oymdwwa 1 40 1’” 6 loop has 004 +3“. ) 2:003) 9 e.‘ FmJath. Eac‘a. (15) Also book pg 216 3, 4 and pg 229 problem 1,2,3,4 (16) Use induction for prove that. 2221““ — 1) = 371.2 + 271 for all positive integers n. cal-L} PUG-”(i (Gh—IFBn‘i-Zw) - I basessi‘l-PI :0.) ;= (jCGEHFB-I‘H-I) M lea! 55:13: £01 “A an.“ 1-4 W“ c' L l u. .C lhdouc} be S “09 43-? M ff;:3(h‘_011 205+”) (*5 +4.4, _________________ P4912. Poe-H)“- ( ‘2 (GE '2.- P700 : 2‘ (62.4), CCnH)—l -C(k+l)*l = 3y; 4-9994—5- k&quot; um: 50m; HM): and. (5‘3, PM: P0») ism ' 1.0..” p51,.“ In @3313: 1. w W)&quot; (”’4”) 4“” le‘f- 5W7 roe W M w, “.2 ii”) . h . ”’lmowﬂiziﬁqupch) 4's 1w»:- ﬂat '44 We&quot; M“? {Blow- yochn):= CM+l)-'73 ‘ w w mot.- (mm)!eh'.CM+l) &gt;3“‘-(a+a).&gt;.. 3 ' 3 :3 --————- e \E'ejH/ “H73 61 ”CE-7' ...
View Full Document

• Spring '06
• Callahan
• Math, Arithmetic progression, Continuous function, Geometric progression, Review Exam, Mohacsy, blank statement

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern