MAC2313_Test4_Spring2008_Solutions

# MAC2313_Test4_Spring2008_Solutions - Page 1 of 5 MAC 2313...

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Unformatted text preview: Page 1 of 5 MAC 2313 Name Test 4 Date: April 8, 2008 For full credit, clearly show all work that justiﬁes your answer. lzx+z 1. (8 points) Evaluate the iterated integral I] I6xzdydxdz sz 000 a a O éXde/ ‘: éxg (We): Q76 2 r Q'X‘E a 802\$ x22 *éxtéBXX “r (2132 + 3x929} i0 = 5.2% 2. (6 points) Suppose E is the region in R3 that lies between the sphere of radius 2 and the sphere of radius 5 in the octant in which only the y-coordinate is positive. Describe E using spherical coordinates. Qé€é5 Egg: e>s IF U. 3 g (jg-7r“ Page 2 of 5 . (6 points each) Determine whether each of the following vector ﬁelds is conservative or not. If it is, ﬁnd a function f such that F = Vf . (a) F=6yi+xeyj P: 8"! Q: X67 29 :: 8y: 7%": 13> F is cpnéervméwe 3X ~‘7 “ 2 Y . 4 {A 14 F ‘px'P E. I: 22> p: XC‘Y {s A Fiféuéﬁi pk eta r Qgere ‘ _h 32 (b) F=(1+2xy+l)i+x2j P: H314” t); 0*“ x c 0% : 37¢ "'3 3'7: 1:?) F is CpA‘Sﬁf'g/gfélv‘er L ‘ 1Q:P:\¥2’)<Y +12}??? 10: 1+!XD’V {Mai/X4 LS é {ii/ta: 'xa PDECAky‘A/Q Caddie/x Fl (0) F =< ZZ,COS(y),2xz > .3 J k “.7 CMFQ 2 2 __. <O_o)azv;}2)o~o>ro Mm 2x; 3:37,: :5 consermét‘ve Q = 23 ~ £11: @5993} :57 10: ’szt— SMHD £5 a Patmﬁ’E/é gag/2144 1C; 7’ 21% r . (d) F=yi+zj+xk CNIJF5: 7:3,, 3?; : 40"! 3:37 F (IS A05 comsermézm Page 3 of5 4' (6 POimS) compme div(F) Where F =< 22 ,cos(y),2xz > .. .9 N7 Oilv (F?) = V‘ F 2 gall? + glad?“ i— %E (ng\) '7; O -— Stab?) + 37C I 9.1 —- ShﬁCWB 5. (8 points) Evaluate JZxds, C where C is the path along the parabola y = x2 from (0,0) to (1,1). C", «2?: “1,1378 Oé’xi-l wig: than“ d9: "4‘ J‘i‘x“+5 of“: 6. (8 points each) Evaluate IF - dr for each case below. For (a), (b), (c), and (d), you C may want to refer back to problem number 3 of this test. (a) F=eyi+xeyj C is the path along the curve given by y = sin(x) from (0,0) to (71,0). -—7 Ext 393‘ F=€79£ when. 10:: ‘xe‘l' .‘ S ﬁhdw : pom“- 1C‘(o,o\:: T Page 4 of 5 (b) F =(1+2xy+l)i+x2j x C is the line segment from (1,0) to (1,2). .. _. § 2 ‘ 8‘1 30:93) F577? Mum; {=- ’X‘f’x'xj +6494 SEEN» {303% NW C ._ .—..- mam» <v+o+03 ~ 21 (c) F =< z2 , cos(y),2xz > C is given parametrically by x = 2008(1‘), y = 3sin(t) , z = t, and O S t S 7:. BY 3m}; (E71675 an. pzxzai» \$5013 t Saga) 0 (9.03:) Fiat?” :: C(Qﬁim - “9,0503 If mm c, 2&2??? 0‘} - CONDW : “QTY-a (d) F=yi+zj+xk C is the line segment 130m (2,0,0) to (3,4,5) ' 8‘1 F VS Mi» tomﬁer‘ vm‘i‘tuo SEW}? :2, 8 Pole: + @951”; 4:: R4; = Q’Mx ¥ 3413 + x42 0. €- “ PM: (mm «now» + Hams» 2 (mt, “H3567 oats: {thipt ’K/‘r‘it 2:56 Oéééri pix-3A4; 5&3?th dargdt C; 3‘1?“ S|Et +— 5m» + (amﬂs‘ﬂ a“: C. * ‘ ' - 3“ to :2 ‘13.. ~8<€Mt + it)» - 3 'F a“ D (6) (f) Page 5 of 5 1?=<)ﬂcoqxxx2+2ysnmx)> C is the triangle from (0,0) to (2,6) to (2,0) to (0,0). P: «faggot» :- xﬁm spam 3%3 '3 9N; Lasixﬁ 3% '3‘ 27: + “Dy cogéﬁX “ CW ‘ ‘25? , “a Fwd?» ....£§3_ S<m 55‘) will Q ﬂare». D a 31:»: t '“ S 9% y 01X o q :2 3\ _ F =< 3y—esi"‘x>,7x+,/y4 +1 > C is the path along the circle x2 + y2 = 9 using a positive orientation. P: :23 «am 0-: ’72 + Jr“ 62 355: 3 % :7 “‘7 M Greg/us P M ii 3i *‘ n77 933%“9” 2K 3 .1: S S L; parole O O ...
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## This homework help was uploaded on 04/21/2008 for the course MAC 2313 taught by Professor Paris during the Spring '08 term at FSU.

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MAC2313_Test4_Spring2008_Solutions - Page 1 of 5 MAC 2313...

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