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# Test4Solutions - Name ﬁﬂjj wﬁﬁ‘“{Z/E I I...

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Unformatted text preview: Name: ﬁﬂjj wﬁﬁ‘“ \{Z/E I I Section: ,Math 234: Sections 1-8 Test 4. k April '26:, 2010 The exam 18811 partial credit. Flease wxite neatly and clearly, showing ail of your work. No calculators, cell phones, books, or notes may be used. The testueont‘ains 108 possible points. Good luck? ‘ Question 3 Points m 1 | 13 i 2 1 15 g ‘ 3 l 17 " a 4 T 15 4 5 i 25 . 6 15 a i Tote}: 100 W I Qwié‘é‘ % " \$2.; m I 3?? .' (13 points) A wire. with variable density sits inside the xynplane. The wire is given by the curve 3; : Sinr, O E :5 E 27!”; the density is: (river: by 6(32, y) m .T + '52. Set up integrals (do not evaluate) to find (a) the iength of the wire, (b) the mass of the wire. Fug-3 :2 5%; m {7? , Oééégm W , ., / i «a r V/{} 3%: M d! f MK it?” WWWWWW ”W mg m - t if. mm :1? f _ m WWWWW z 3-: i W i M -~ Mwm -; 6' E In»: \$22 z ‘ -_ Wwwmmswmfmwmmm? 53' W“ - (E “i" MM"; i M 4*? fig. #13: ﬁ' 3"”? 2. (15 points) Let. C be the straight—line segment going from (0,0, 1} to (3,1,0). Cakuiate /(y2+2)dm+mdy+(z~1)d2 .c J '3' éﬁsggfk? “’3?“ ”ﬂag? a Wig} 32:. 4 ’g"{“ g mgr? f wﬁéw > §iif§ jg; “a 3? g Ltd’EéZngﬁg I-‘L— (X4 c, - ”a; + (Eva‘s 9% _ 3-. (17 points} Let C‘ be the curve given by the inﬁzersectien 0f the plane .1? + y + 3 ': 1 with the ﬁrst octant _ ' (orientedcounterweleckwise whee viewed from above). If F m 2973i —i~ myj +yzk, use Stekes" theorem to- c'alculate the work done by'F aieng the curve C“ Netti? m. (wig-g”. eﬂgg g \$5};qu ﬁlm. We: ‘iﬁéﬁeg ﬂame gag. fwﬁ‘ éz‘mjygﬁw if}? fﬁwmvé. ”\$3me 4. (15 points} Consider the consemative force Fr (yz + 21' in: 4: 211.561; +12). (8 ) Find a potential} function for F. (13} Find fCF'dr Where C is a curve starting at (0,0, G) and ending at, (1,1, i). 5. (25 points} Let S be. the cone 22 m- 9:2 9% 3,12, 0 g z 5.1. (The cone does 110’: have a, top.) (a) Fincﬁ the surface area 01“ the cone 5. _ (13),;de the outward / downward ﬂux of F m (3:, 3,1,0) over S. £7 5;" “Elli-”VFW; ' u c? _ ”L, I? I.» Q .géjwﬁgﬁgw méw ‘7 :5; 34 Mai” 33\$ ' a. “E; g» i « ”mi" “9% w” ' " m m @3399 5E 3% ii K 13mm ﬂiﬂmmwigmﬂﬁwﬁi‘ﬂw‘dxﬁw’ﬁN‘lﬁWﬁ’ﬂm? 3 . 6. (15 points) Let S be the surface whose top half is z m 4‘3132 m—Byg and whose bottom—half is z: m2 +y2. La%' 2 (3:2 + 333, :2 — 2y, 32 + 22)‘ Use the Divergence Theorem to ﬁnd the outward ﬂux fjs F » n 030. 0 Y ‘ifay Zea/us you?" answer in the form of cm iterated integraé. ...
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