Exam2_sol - MATH 234-0 Multiple Integration and Vector...

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Unformatted text preview: MATH 234-0 Multiple Integration and Vector Calculus Section 67 Midterm Exam 2 May 15, 2007 N :2. E I i _‘. ame: ; - -* Dela figmg Instructions: 1. Print your name on each page. 2. Show all your work neatly for full credit. 3. No calculators, notes, or books are allowed. 1) Find the moment of intertia Iz (calculated about the 2 M axis) of a uniform sphere of radius R z 5 and unit volume—mass—density pH") 2 1. ( 16 points) :5; =1 l W W254 «fig/W“ “Fm l I} \ m x?“ M . g : , i i%-: l 8 3 (mm was j; {few (in (32525 ale :3 fr _ ‘37” 8‘ - 3 ‘ g M53?” :2 ‘" of?” Seafié (M gfi ‘22 H “* (pl: rum? 1%": 2W1? 3 {£25 E! E} f Nam ) Find the surface area. of the part of the paraboloid z m 10 — m2 — y2 that lies between the two planes 2 : 1 and 2 z: 18 Name: Jg {hfifgggfl 3) Find the divergence and curl of the vector field 1312:, y, z) m (way); + (2 sin + (myln (Show your work) (16 points) a: A: ’m “W ‘ vs 2::— Qik )6“ 3.3:; .1. 3% fl 26mm; &3C (91’, M3 “3 A Va, 1: m 3% s, 3% {26% 3.. 4) Find the area of the first quadrant region bounded by the curves 3; 2 m , (18 points) Jfliak 1 (is/gadgj’ik 6231!}; cum "; z E *4 z: a a?) [UL {0'3} 2 y : 23:2, and x : 312,51: : 4y2. x it; L w L)... 2.; ‘T “w? "L 63131)} ‘g‘év “F36” 4 1 s- 4 fl “3. a“. '——. _ ’43.... cfimoflfir ggflijQQ/‘m g I fling» 3mg“ ‘* X] 3,me i :3. 4 1,. 4 I .2 km: :3» 5,, :«Lwr A HEW/13 egw‘ow 6mm Name‘ gdflgmg 5) First determine Whether the vector field F (32,31, 2) z (1 + yew); + (2y 4— we“) is conservative ( showing your work). Then, if it is conservative, find a potential function for the fieid (16 points) “3 , e .i fix F :- fi [ghyaéh (5% 1?: ,_ if 23$ Lenwvafiim 995 fl We; WW“) 3 A , _ M35 , b Wife X t J m: .4 3x .. 3% fmsfiwdf cfifl My ' ‘ k—ommwwww “WWW; 9;f: Fig 4-"Xxéwk: 756%4 W 9% 3 9 ‘9? 92 I EMMWW % , K be gfiwg): 31,4314» ax? + $sz 6) Evaiuate the line integral [IE-d? C along the curve C, where 15(33, y, z) = 2;} + - y}; and C is parametrized by :1: m t, y : 152, z = t3, 0 S t g 1. {16 points) . F ~ ; #1122»; awwu, c {3 Ecmctflfiijéwmafi’l? RM :2: girl) £13) 3 i ' A in E * Q (J'C’ijc;*{”)“ {1) 3% 3 36) an,- ...
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Exam2_sol - MATH 234-0 Multiple Integration and Vector...

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