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midterm 1 solution - g 0\er CW\S SIMON FRASER UNIVERSITY...

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Unformatted text preview: g 0\\er\' CW\S_ SIMON FRASER UNIVERSITY MATH 155 Midterm 1 Last Name June 3, 2009}, 8:30 — 9:20 Given Name(s) SFU iD Student signatu re INSTRUCT¥ONS 1. Write your East name, given name(s), and SFU ID in the box above. 2. Sign your name in the box provided. 3. This exam has 6 qoestions on 5 pages. Piease check to make sure your exam is complete. uestion Maximum 4. This is a dosed book exam. 5. Graphing caiculators and caicuiators with keys iabelieci f or dz: may not be used in this exam. 835k: scientific caiouiators are permitted. 6. if you need more room for your answer, use the reVerse l . side of the previous page and cleariy indicate that you have done so. 7. Communicating with or intentionaiiy exposing your written work to other students daring the examination is forbidden. 8. You may lose marks if your explanations are in? complete or pooriy presenteé. mmj MATH 155 Page I ofé' 1. Let 7?, be the region of the piane bounded above by the curve 3,: m 9 — x2 and beiow by the curve y ..—.. :2: + 3. {I} (a) find the x-coordinates of the points of intersection of y m 9 w 3:2 and y m :1: + 3. fire Curves imzasecn‘ Lake/W qwz'“: 7M3 _ m) 3M3 or 7331 [4] (b) Express the area of R as the limit of right Riemann sums. Begin by finding expiicit formu¥ae for Ax and 1c,- in terms of n and 2‘. {)0 NOT SiMPLIFY YOUR ANSWER. AZ 7.. 2.--(-3) .3 5“ M h n Vamw3+iaxmw3+§g n On; ‘hne mkrvd (“’3 ’L) We. curve. ym Cl‘fix has (Agave. “\MQ CUJ'UQ. y“ 7H3 -~——> mm a0 1% m gawk rs (w?) ~— (n+3) ’1 Arm :2: hm Z L(q”7(z1'3 “(Xi—+331 AX {144:0 ”- MATH 155 Page 2 of5 [2} (c) Express the aréa of ’R as atdefinite Entegraf. [)0 NO"? EVALUATE THE ENTEGRAL. r 2- l m 7- ._ Am 2: S (m x \-~ (M3)) Ax * 3 [4} (61) Write down an integral that gives the voiume of the soiid that resuits when R is rotated around the :c—axis. incfude a sketch of the region 72 together with a typicaf washer and state the radius of-each circie. DO NOT EVALUATE TRE INTEGRAL. ‘I Y$1+3 OuAer faékiufia 0C beaker 3: q” 7i?” Inner “Ame of “maker 1"» 3 "f 7G "31) Sea-GALE. acres; (.30 one. Stcle. 00 *1“, maker is «r; (0‘..fo ~— “a (9*?ch Tktekness apex-SK“ \} \l flame. of M5“! 1’ 5 M "kawcvmfibx MATH 155 ' Page 3 of5 {3] 2. Find the average vaiue of the function flaw) m $2 + 1 on the interval} [3, 6]. 6 \ 1 10M ”‘2 338“ mm .3 c, a: 33‘. 35; >r {X3 ... \ ._.. .— «SKU’MQ GHQ—X m 53 @343 v- 11 5g_ 5:2 [4] . 3. Soive the foiiowing Enitiai vaiue probiem: do: w x2 + 2’ MO) 3 1r. 2. ' 7. m. '74 ,... ,._ VHS 1-H C)“ .__ \CX“M\ “M: a“ x X‘M “*Sw :3wa T“ 1"”Cx‘fiwllflxw7i J“ C mkegn 17—0) ‘Y-x’fi :0m6gfk'kéwx 0* Q1: C; m QTY—”TY Tke Solux’ion 2‘3 1/2: ’Xwaft‘éénfi +'TT ' MATH 155 Page 4 of 5 [2} 4. Simpfify the expression % / sin(cos(t)}d£. Gun («:5 (€33 . ex --- s L0 (L08 (x‘\\ -'2. 7s 1 o 3 {2] 5. Given that / f(:z:)dz 2- 4 and / f(a:)da: 2 ~10, find the vaiue of f f (z)d:z:. 3 3 1 3 \ S ()8er “I: \O ‘3: Sepcmch A~ S3 (3&0ch MATH 155 6. Use the method of substitution to eva¥uate the foiEowing integrais. exflfl Page 5 of 5 {4] (a) j; ”(imam LenL Wm M?!) duw é—{CLK I (—Okem 7V7”) unO ”“77... W‘hem 7— 3"" u» 1‘11 :wa m _ “~31 g‘fii {7‘1“} ~57.7<o\7< “-2 gLu-fi) Ukw ("Xxx “— \QJ‘“ 4.. “\03 A“. w... 1 t “ J; “335.3 x—L '1 Wm H. \\ \Z ...
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