Exam2_sol

# 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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## This note was uploaded on 09/29/2008 for the course MATH 234 taught by Professor Boeri during the Spring '08 term at Northwestern.

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

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