Sol-162E2-S2008 - MA 162 Exam 2 Spring 2008 Name Set/w” 0...

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Unformatted text preview: MA 162 Exam 2 Spring 2008 Name Set/w”: 0 M Key 10—digit PUID RECITATION Division and Section Numbers—w—m— Recitation Instructor Instructions: 1. Fill in all the information requested above and on the scantron sheet. 2. This booklet contains 17 problems. Problems 11 and 13 are worth 5 points each. The rest of the Problems are worth 6 points each. The maximum score is 100 points. 3. For each problem mark your answer on the scantron sheet and also circle it in this booklet. Work only on the pages of this booklet. Books, notes, calculators or any electronic devices are not to be used on this test. WP MA 162 Exam 2 Spring 2008 1. What’s an appropriate trig substitution for the integral / m3 V 4 ~ 9302 dry? Jafwéfilxj) i“ wax) Lef (MK) :3: 6C 90v» @r .358 : 23in(0) B. 351: = 2tan(0) 1:; 3X :3: Z gi“ (:9 C. 3% =2sec(0) D. 2:1: : 3 sin(0) E. 258 = 3 tan(0) 2. Using an appropriate trig substitution, the corresponding 0 limits of integration of the . 3 x3 Integral \/§ m d3; are .91 . W , >1; 7r/6 W We x: 2mg flew gar/m a. 7r/4 .4 F; M “i ”I! W “I? B. MEWW {/5}qu (€>“’ é? QM 7r/4 A. 2 w ‘K w CIT“ 0' 7r 9<?\:m(3)“tm(l)”:}“ :3 D. 7r/6 E @ "2* L .fi {3" E ”/2 E I , '1 ' - 7r/3 J \ 5 3. Using an appropriate trig substitution, / $:_ 1 dzc = $2¥Wi “:33 X: gefi/G' A. /tan(0) sec(0) d0 WW szwfi'i f; ge,c,&."mi 12 W27} :: firm-g B. / sin(0) cos(0) d9 WA (AX :: £63“ (9' ”(Lfljflélficéfiw .. C. / sin2(0) d0 YNZW“ W k w $609 ‘JfT/"W9¢8 D. [sec2(0) d0 wwww )4. W p K ‘19 we @/ tan2(0) d6 : j “(fl/AM, '“ 6} .La» MA 162 Exam 2 Spring 2008 1 / 2 4. What’s an appropriate trig substitution for the integral /-—3—— 4:1: 90 Z Z _ = ' W” X :3 ’(74 wflg‘zfi 4,ng +LF A. ac 2 m3s1n(0) W "L B. m—4:28i11(0) W Li ”(3472) C. w—2=3tan(0) 900. mi, X—IL 3: 1 Sim S, :1; ~ 2 = 2sm(0) E. :1: —— 4 = 2tan(0) 5. The form of the partial fraction decomposition of $16326 is ‘ Nab/x. Aac+B Ca3+D [(0 2?: pm W A. m2 _4 + ($2 ~ 4)2 whit (>4 - L68 (\A 41+} B A + B J Hz) LX, in ~ 4 a: + 4 1 C. A + B + 0“” + D (X'L\(%~+QC\A Jr?) a: 5 2 a; + 2 9:2 + 4 ' —- 2 5 A E CHE 5” 2 w + 2 a: + 4 /1‘JM err W A B X”; X42? nytii’ E' x2 — 4 + m2 + 4 3m 6 (:13—1)(:v+2)dm_ 3x A? i £61n|w11+21n|m+2|+0 MM” 1:: W ,3 B. ln|m~1|~2ln|m+2l+0 (xAfl\)L\[g‘%‘2«\i X’Wi fi#:/N’m 5 C. lnlm—1I+IIIIIB+2|+C W”)? 2 7“ ifiviwifi£ffia#EEL:->Wd””W”’ D. 21nlzc —— 1| +1n]a:+2| +0 “a; L we) 2 3 %I&\ kO’E EMA? A, 2' E. 21nlm—1|—21n|ac+2|+0 MA 162 Exam 2 Spring 2008 1/ 2 _ 7. From a table of integrals, it appears the integral / 9:321: 4 dzv is closest in form to 1/ 2““: 2 2— / u u ___a du. With an appropriate substitution, / 1? dm : ~ l 1 m ’ fl \ :1; h—v LL . '- M”VLf2xWa-Z.m .3 A4/T d“ , .L m6“ DE”: 3 “b“ ; 5” CL" 7% CL“ B. 3% Ed” W‘Mwm‘ M“, J v ”flmuV - " ’ Mfi V:— ~ L 1 “2 __ 22 L Way L __ (MAL i i U ’ "Nut @12/ u d“ MM x L , {bk \2( g ”l W D 12 / du u MT: 2 2__ 2 ’ \1 MW‘””“*”‘ 3 u, , UL 8. A pool, 12 yards long, is shaped like an oval. The distance, in yards, across the pool, at 2 yard intervals, is shown below. Find the DIFFERENCE between T6, the trapezoidal approximation of the area of the pool and M 3, the midpoint approximation of the area of the pool. MgstfiEr’lrSl 1&8 A. 12 ‘10 0.8 D.5 l l | | 4 I I 024681012 E-2-5 MA 162 Exam 2 Spring 2008 Z 9 [15% gm :7; “AZWK‘ AW? B ln(2) .2 M1. E ' 4 5 D. E E. Diverges oo 1 _ x t“ l , ’ A. — W“ [1 " it" 16 w my M? I B. ~1— fiW? Mwfil) { 128 1 w :Lw ,i-L»\:o+ri— 0'35 ;.b—=>>00 LILQfi/AZ 6%- Co%’ 3611 11 Find the length of the curve y: 3 + 2333/2, 1 < a: g 2. W ngik W i bmgflzg} 2m i&.22—7(193/2—103/2) l/ ‘27 \W\W éfi: W [+(gX2’YW: Lqux 1 3/2 3/2 Qgg 7 , 3/ r , C.§<21 —13 ) WWW kafiflMwl\p BM” & l/Vvflxgfi 0] ,1 E 4¢§+1 3/2, 3/3,) ; 2,7 ( Vi WW MA 162 Exam 2 Spring 2008 12. The curve 3/ = 3:5, 0 S a: g l is rotated about the y—axis. The surface area of the resulting surface of revolution is 1 1 dS :\/{ + “/2479 CM A. / 27rccx/1+x10 dm 0 / Ll, 7... 1 _. Li’ 534 > AK“ B. / 27r$5V1+$10 drr I WM g wwwww Dix @fo: 27rmx/1 + 253:8 da: 0 D. 27m: 5\/1+25m8 d3: { 0 1 E. / 27rrm/1+5a:4 dx 0 13. A plane region is bounded by y = 932,31 2 0 and :1: = 2. Find the yfizoordinate, ‘3], of its centroid. g L 4 {2' .2 M __ 4 3% K Kg @ Ay:g E _ 2 “33”,? 9 , B F5 ‘ L q_7 fag :X Swill/K (”—3 6 3 l {Mi ’6\ jrwwzéfrw am® ‘QI H 2 w tog} /<> // “l 14. A plane region in the first quadrant has Lentroid (3, 4) and area 7 square units. The volume of the solid generated by revolving the region about the line :1: = —2 is m&i\V‘-5 5: 3 ”(”39 :3; S” A. 8474' cubicunits \ l /\ 670% cubic units 2W2; Vugmm 0’ g DOA 4, [Fa/b (”(le C. 567r cubic units _, D. 4271' cubic units '7 21F (g >67) :5" 7071’ E. 3571' cubicunits MA 162 Exam 2 Spring 2008 n2+1 71? 15. Determine Whether the sequence an 2 converges or diverges. If it converges, find the limit. 2 9:»; l A. Converges to 2 \ .7 , \ VV\ 1“"?in :: IL Converges to 1 WV‘ 00 V\ C. Converges to 0 D. Converges to 1/2 E. Diverges 16. Determine Whether the sequence an 2 sin(n/ 3) converges or diverges. If it converges, find the limit. \ A. Converges to 0 \ M00 QM (jg—LB dgg}; Wj‘ Q/fd Sf“. B. Converges to 1 \(\ -=¥> C. Converges to 7r/ 3 \/§ ”a" i 3in [/%)E A? Vflj‘a; D. Converges to 7 @Diverges. 2n—1 . converges or diverges. If 1t converges, 3n+2 17. Determine Whether the sequence an 2 find the limit. 2 ”i A. Converges to — x V\ v jflm Zia—«~— 3’ fi‘m (2) ($3 ‘ B. Converges to: VV’5 00 3M+L “”370 Mfg; 1 Vi @S L 3 3 C. Converges to 374— V\ Converges to 0 MA r VLW i) :_ O E. Diverges. ...
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