152mt2-1097-key

152mt2-1097-key - SIMON FRASER UNIVERSITY DEPARTMENT OF...

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Unformatted text preview: SIMON FRASER UNIVERSITY DEPARTMENT OF MATHEMATICS Midterm 2 (v.1) glut .77) MATH 152 Fall 2009 Instructor: Dr. L. Goddyn (D100), K. Doerksen (D200) November 4, 2009, 8:30 - 9:20 am. '/ Name: /K' e (please print) family name given name SFU ID: student number I 5FU~email Signature: Instructi0ns: . Do not open this booklet until told to do so. . Write your name above in block letters. Write your SFU student number and email ID on the line pro- vided for it. Put your signature on the line provided. . Write your answer in the space provided below the question . If additional space is needed then use the back of the previous page. Your final answer should be simplified as far as is reasonable. . To receive full credit for a particular question your answer must be complete and well presented. . This exam has 5 questions on 6 pages (not includ« - ing this cover page). Once the exam begins please Tota; - check to make sure your exam is complete. . No calculators, books, papers, or electronic devices shall be within the reach of a student during the examination. . During the examination, communicating with, Or deliberately exposing written papers to the View of. other examinees is forbidden. MATH 152 Page I of 6 1. Compute the following integrals. You are encouraged to specify the integration technique used for each integral. [4] (a) / tan298ec49d9 l _ L Si-lésf/i/[u/e LL; {an d“ : 556 1? (1'70 13 (2L1 (ME-H) dam 3 _ ' {gusrf'gu .tc ,, \i ‘ 3 3 a 7% We 5’ t {can (3/ .,L C MATH152 Page 2 of 6 2. Compute the following integrais.You are encouraged to specify the integration technique used for each integral. [4] (a) fmdt 556 (V 7-) :c+2 [4] (b) fwdx [any (IEV’iJl‘EK 1.1 +3 I _ “DC-+1) 7.11 + 7/11 + 7 3 L1. +3 ‘i’ DUDE {/J‘ 2%?“ + qJL _M 3% 4'? 3.9L 4’ 5 A4 [Vii “t C "L «3 DC +3Xt : MATH 152 Page 3 of 6 2 1 566 (V11) MATH 152 Page 4 of 6 3. True or False. lf True provide an explanation, if False give justification (for instance give an example for which the statement doesn't hold). [2] (a) (Ex—4 A B can be put in the form — + for some real numbers A and B. [332+1) a: $2+1 .526 Z) DO [2] (b) The improper integral / 8—1 d1 converges. O . Set; (ll/:1) - [2] (c) If P(:E)/Q(a:) is a rational function with deg(P) < deg(Q) and Q(:z:) factors as a product of distinct linear factors (2 — 0.2-) then f P(:z:) 62(33) d1: is the sum of loga- rithmic terms Ai in(|x — ail) for some constants A:- plus a constant of integration). See (v.1) [2] (d) If [:0 f(:c) dr and famgkc) dz are both divergent. then fax + dz is divergent. gee (“-1) MATH 152 Page 5 of 6 1 [5] 4. (3) Use f(x) = as 6 [1,5], and Simpson's Rule with n = 4 to approximate the area under the graph of y = flat) for 1 S :c S 5. Note: Put your answer in the form of an improper fraction. / [3] (b) Let Sn and .310“ be two Simpson's rule approximations of f(:c) due, by using n and 10p, intervals respectively. Suppose Sfl can be trusted to 5 decimal places. How many decimal places of 510” can you trust? 52:96 (V- 1) fl'fATH 152 Page 6 of 6 5. Compute the following integrals. [4] (a) fosmildli l’lffJ Val-'lllfrf/ eijmffir/c.’ t M 1:1 ‘. L dz 3 )L t—vr lr P x t“); t W? “ff”- filg mll l} , Ill¢1 In Ier’:]- : /;mq In lt_d __ L4 I,“ f“? I- 'v’ for _ 12°00 Sc? lmlt’ym/ .5 lv’c’t/y‘c’)’ [5] (b) [To 226* d1 556 (1/. 1) SIMON FRASER UNIVERSITY DEPARTMENT OF MATHEMATICS Midterm 2 (v.4) aux (If. 1) MATH 152 Fall 2009 ‘ Instructor: Dr. L. Goddyn (D100), K. Doerksen (D200) November 4, 2009. 8:30 — 9:20 am. - Name: (please print) family name ‘ given name SFU ID: student number ' SFU—email Signature: Instructions: . Do not open this booklet until told to do so. . Write your name above in block letters. Write your Maximum SFU student number and email ID on the line pro- vided for it. Put your signature on the line provided. - . Write your answer in the space provided below the - - question . If additional space is needed then use the back of the previous page. Your final answer should - - be simplified as far as is reasonable. . To receive full credit for a particular question your - - answer must be complete and well presented. - - . This exam has 5 questions on 6 pages (not includ- - ing this cover page). Once the exam begins please - check to make Sure your exam is complete. . No calculators, books, papers, or electronic devices ' shall be within the reach of a student during the examination. . During the examination, communicating with, or deliberately exposing written papers to the View of. other examinees is forbidden. MATH 152 Page 1 of6 1. Compute the following integrals. You are encouraged to specify the integration technique used for each integral. {4] (a) /tan36’sect9d6 : ié‘eclfi-li 565:: (-23 661:. cf? vii/5) @135 tiniffl i I (A: 55C 7 7’ if; 1 5‘? - 6.3 5,? (My :[(9541)(7{£[ C L ‘LC )‘ M : --———- -—M, ‘i' C i 3 3 arse: e “5666:? + c .- 7 r' ‘f' [4] I fetSintdt 1.7: [Dds‘I/s UL; flit: L: {I {7 r 1 [Afa— Lm {‘ {f ‘1 git T: e i - jg t w— _ H ' A . r t By Width fifjjciffi V566 (AF: ~14}: L" 3: MATH 152 Page 2 of 6 2. Compute the following integrals.You are encouraged to specify the integration technique used for each integral. 1 _ [4] (a) /t2+2t+2 dt Camfl/Wzfi 'HW .Sf/v'ilffi‘i . '1 I, “571406 b-‘v/QC : ('0 (W H [4] (b)/t2+t—4dt - -. l \ t+3 QIL/Af/C/Vk ..(:_7‘ . 128) z. g ml. m l; "‘t ‘/ 2ftng '5” 0“ (“Mt : {1:215 +1 /m [6+3] + C ‘15 ‘é MA TH I52 [4] x; 1 .M . , v2\/,U2—_f dv .5“ Page 3 of 6 U:- 56: V,“ 3 £7?“ (7‘ Why“ (f: 122:1 0:17;» / ‘1 V’Z'! "g 1 if ._ 'Tf' I L if V— 2_ 1 Cf, 5)C?‘1I’3/1‘V1%§/K=at/ If [ {73:4 . {C712 9 0(6) _W L A‘ . "Tr 55° 9 ,/_ ‘i “6’ .,_ {729-1 , ’ A d 6(6)” 63 "2 I, “2 W: : . m 3 551 cf? 1 f5“ Q (15; 3 .— l _" “I fi- ,. 5H1 A! 7’2! g ‘n’ S {1’ .3; 5H4 *-’ Jun 4' 2. M; "V; w .5 l A L’ 3 _ [/ZI I 5" V 73 2x MATH 152 Page 4 of 6 3. True or False. If True provide an explanation, if False give justification (for instance give an example for which the statement doesn't hold). (a) x m can be put in the form £ + B (332"; '1'“) a: 332 +1 for some real numbers A and B. . ‘L ..._V I , d . I f» /l ha /5 € {763651 “5/? f» - B :— f” i "LB L m .r' ‘“ X. 9th» I )L (A f“ I) {flit .575 ff “.1 C7 . . B -- I he; we 16!»; firm: _____...-_—.-.._.._.., 53 MM [2] [2] 00 (b) The improper integral / 6—1 alas converges. o ii P’— .\ f w r -l l‘me, .51“? lim { e 10%, "1: Am ~61] few 0 {gawk} - {a -\ "LL ~. . "E 2 l2: we :i (c) If P(a:)/Q(:z:) is a rational function with deng) < deg(Q) and Q(.t) factors as a product of distinct linear factors (a: - at) then f P(x)/Q(x) rim is the sum of loga- rithmic terms A; ln(|2: w ail) for some constants A. (plus a constant of integration). [Pl/if Sld’tf'g . (we) .___.___—-4 f0 a; jam (PK fawn/(5 If); e'L/flCZr/JJ fig/“Ail / 15V a 57/; (fl/1 5‘ :" Wt X, - (L ; (d) if fawffic) dm and faoo 9(22) dz are both divergent, then' fam + dz: i5 divergent. J 70er excxwp / ({mflK S _[ fhém I jawed 9° ‘9 0‘, .6.» I/‘(ewéqm 7:. gm = M (0-0) a 0. m. ‘j d‘ a 2% gram (P MATH 152 Page 5 of 6 1 [5] 4. (3) Use f(x) = :1; E [1, 5]. and Simpson’s Rule with n = 4 to approximate meek under the graph of y = f(:i:) for 1 g at S 5. i I 3 v.“ 3 “my Note: Put your answer in the form of an improper fraction. ./’l:'/’\6(,‘t 4“!“ S1 A“? _ f L “ 3 (PM * “i lea-r 1 lea) t WM) t lml ,/ ‘L l :J-v(-L“t it fill—(1+?) 3 l 1/ 3 i1 5 , w, _ - L “L3: r t LE: 1‘ w: 3 )4, I5 Is ls l) I ' — ’g ( 15’s,, e 73 ‘if [3] (b) Let Sn and sum be two Simpson’s rule approximations of ffflx) dx. by using n and 1071 intervals respectively. Suppose Sn can be trusted to 5 decimal places. How many decimal places of 5'10” can you trust? Wt}, aft/e 1/923?” ‘H/ixll fin/Wm" 0/: if all waif 5 " 5* was” Klilsm 5” O M The (2 VV (1' V" g} F j [genre {Ll/e a era’f— _ . 5, mm . ‘ 5’ K [ . ~ 6%) : {mew-L) f “2-— Li I Q (It? m)Ll mil - -' _ w"i’ 4 f0 5“ f0 7 “~—‘- M“, H immemmwayhmflmamm MATH 152 Page 6 of 6 5. Compute the following integrals. [4] (a) [fring ’ 3 t dim 1: l/WL lit-1 f" I'll/1+ “"1 tag“ ° tfil C ? t ; I’M Im [1,1]] +- [IMF ln [Aral] tfll' . "0 {fig t g:— w w w e l w Ely-H; mil: 57/49 .221 it; ‘lL (L: - 50 EA E [314 ‘llf'ya/rg/ dflV/thyr’ (’5. ' [5] (b) [0 me‘mdm f, ‘1 .5; 4'- 13“ LLLPL U'irff- l ‘9( «BL. *1 f_ ‘ a. J3me d)» : '-,>ce]- [*6 a!» ctr! U=~€l 0 U ‘3 - . '-)C -:c f : “ace + (-C .- -t -13 *0 ' “f E’- -—e - (0—- e ) u. «t ~15 ~ {*t8 -6 50.70 f A. __ at g I .15 (It 1 AM fig (ZR - film”! I— ‘C tfim [-950 0 v ...
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152mt2-1097-key - SIMON FRASER UNIVERSITY DEPARTMENT OF...

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