exam3_review2

# exam3_review2 - 53M 31‘ Raview Problems 3 1 Chapter 4...

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Unformatted text preview: 53M 31‘? Raview Problems # 3 1. Chapter 4 Review: 32 2. [a] Using the Divergence Theorem, show that the volume V of a region T hounded by a surface S is given by 1 o = a f flrdyde + gaze; + zdrdy} S [h] Evaluate the above surface integral directh.r for the parallelepiped. [115:5.3,Diiy5lilizﬂltoﬁnditavolume. 3. Chapter 4 Review: 2'? 4- S is the disk shown, and C is the circle bounding it. Elm! y: z) = 23: "' I} + 3E (a) Evaluate I = f h - 5 directly. :2: [1)] Evaluate I using Stokes' Theorem. 5. p. 522: 31 6. Evaluate ffryedydz + {r+y}dzdr+zdrdy on S : z = 333,0 3 r i: 2,—1 5 y 51. F 7. p. 522: 33 . y .. 1': .Elﬁ_d__...ﬁj.:5§n_£1:{eqs “45'- ..£E15§.n...4.e1¢ﬁf_ceﬂ.t .. {\$131!}.-er ..".' __ r50...) 19, .. 5/. 1.,” ,. , W?_.£.'rsr.__km_nf 1"?“ __t_!fe..n§f¢fm _. £16911: . :13, .. 34.55.91: 4.1% 5.3?th .. __<t'f.__'"k_’it.xu’ .__..i<fr: _.m_.._ie::. .# ﬁa____§a.\$sh‘a‘a.rr::_aa____. _. M 511.2%. " 5/ Le?) f M a); " £43"?- KEEP. = Q. .______ 1-15 frfw.ﬁ._.iﬁ_ﬁo . . “T4: safasegﬁ 'y'ch)"; _ ‘3’“ 1333;“; 95.0)! "*‘r ‘w m: _.._g‘_.rL E's; . L15 ___ __ ___ _ _I _ _—__ _ _ _..__ _ _ ___ ___J__(«_}J : 0 _:?__.)‘_/£ 3 “Vac: &_ c: r: J: _ E .._____._.__.....*. c: 7"“ ...§_r:3_1=_#1_!£:z {FEES 4.461: .. ' ' " ' 2.](Q'Jiﬂiﬂéf Leg :4?" 1' asce'ggiﬂ _T", x: " ' V2355 JQJ; ' .4533; f. ._ " " T " ' . _ J. __ .. . . 92.6%.? .. F: {Jinx/1%]... Warn. "Elf-“Ha, .4“ E- = / .. 1 . ______ i "Z (I???) MAE; EH} £72.29 mg; am)! I I " WA 55?- —- ’54 ﬂu....5&f..’{i¢ 1%.. \$54.. we: _t_1_£_;:;f33 Wag" .__"i”"?? a; \$1154; . f _ 3 53:1 w/t,_ m1 2 Lu; 5: ﬁ._.3_t_»u_#_. €35»? 5-" 3) CI ._________. ..j:,_,_f__5l7ﬂ“(1”!FEE).L-£a‘.ﬂ..(ﬁ'ﬂ_bvfl._dﬁm -3161 3.": I . __________________ .._ If. _ _— _ .. .J_____ .. a “f_2-__cr;os_.(n.£~g4:_ey_+url '.'_...L__C£.s_(ﬁ_ivﬂ:w3}_ﬁr..__ _.__ .. . _. _. 13r___. ______ .. ______._._ .. .71....5ﬂ_-__mi.(AEQZE_;@))".'_'{_lééﬁéiniylg___ .._..__...___._£,«__I -—- _______ Radamjujih 144.4:1_:_€11_).___.T. .6533”)._ﬂh/ﬁmﬁam))fg _ Zﬁwix'ﬁQu Heft?) . G! _ _ r1123 e): 2;»; £1131; e eiéé'ééi _ _. _ "F 1%..-93: ” I ' f: ____ " 1: 5-1 ‘2‘ u 1i w? 13' :4" 5m 1; i’f‘f PI: n: 'w in! id”; 2+: Q? ' VH1. he: - £2493 . 4" 9f 5:". m #1 AW. {1an am 5%: m.) _ _ m a (we? ' 4.5 _ . . a» ﬁ/ f-.¢i[/~cﬂ_~_x[a~23.._v+__%&reca " 6;" 5f...&ii,éé2:¥y22 e 'éréélﬁéllf(aiﬂfa;__ J' I 3:. I ' n ' ‘55P“? cc; PH. _ .7 .5; (mid; juézeyjlélri\$332. f H . +3331, _.£y.? =55? A L f 7-: {LEW alga ...W.'£H*.‘.S ﬁf1gﬁ_ﬂl Hr: Mﬁrrﬁ . \$5.53. 1%- [Q¢....3_z"' (51:15.--. "air .. Ft- £5335) _____ ___:_,_.___, ____ _Lf_i,.[§r_mx1_i_t..yj__§25 ._ELEET? __E"___i_ gar 9-4: __ _ _ y, .22 a " ._..._—_ .L . d_.___, __. _ __._.___.. .. _____:._C&L)Jg..ZELELJ;. .._f_Ld;e__'I_§E3j;______. aﬂiﬂﬂﬂﬂ, 2w; .t._35:g~wj__. ..h_.__'r’__§_£§?._;_%l___._ . _ _____n.,_a_£:.1..j_c;g,s..qu,_:_ng-L_q]_______. _. __. 1" '1'.- _....._.____.. .. ?CE£_KEIhV *' Eric? f1.é(...¢.¢..s H_.__":!_V__C;H __ __ ..__ __. ._ . _ _ 7. ___;f. La: H.701 End? C/L. _ _. . ._..____?7_..3;_ VJ : f I _ ___ __ _ _ __£.i{..i,5’” VFW} Gil-1 ______ _ _ _ _ __=.'. __J Jab: . r"- _ 1r ...
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