# QUIZ 12 - Quiz 12 Sections 16.3-16.4(15 points Math 200...

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Unformatted text preview: Quiz # 12 Sections 16.3-16.4- (15 points) Math 200 Name: 52? .04/30/ 10 Show all necessary work for credit. Group: 4 pts. 1. Determine whether or not F is a conservative vector ﬁeld. If it is, (a) ﬁnd a function go such that F = Vgo and (b) use part (a) to evaluate [CF-d8 along the given curve C. F(x, y)=(y+2x)i+(1+x) j; Cis the line segment from (1,2) to (3,4), g) Since ‘Hnr Aemaim o? Ff}- is snarl: —Ccnnec+jd~ atch - Cwltﬁ) = §X{HQ-§}(7+2’):I_I= O 9 F [S c. (onset-o‘th Lieder ‘Fk-OIJ. To 3;”. (p: [m 33%,)6-71' 1: I @lijJyrlxdx = X) +K1+3W w. £34917): H" 3 Lay/(K) Hugh/l): x+j£ﬂ=x+l =>3lfvl=l ﬂare-Fore 3/7):53’1y)47 : jl'dy = }+ C. “a 7 and C9099) =xy+x 37+ (- u CSF‘dj : [mp-or; : 4N3”) «(190,13 : (11+°I+’1')~{2+l+l) I 2'5 ~ 5' r 20 m2. LetF(x,yz)z<3+4xyz,2x22—y,2x2y). Compute I: J-CFods where Cis the segment joining the points A(1,0,1) and B(0,0,2) , together with the quarter circle centered at the origin and joining the points B and C (0, 2,0). The integration is performed from A to C. Snare ‘Pm! clematis. of"; is Simiala ~C6nned-eoL and Cur! = j E 1 1 .3 5x 5%. ‘- <1x-leixy-LtKyJ th§-er>=0 ) 3+Lh‘ﬂ sz-y) 1X1): F 3.5 Pa. Conserucriih‘e v€c+0r {fetch . "’ ‘ . 3 lo and). Us; :xcp :3+‘+x71:CPIx/zg):j(3+n}gyg)dx : 3A+2x>3 43mg) Um <I> =1 ‘ - ‘ 2. r )y Xi‘ 3 . >7(9x12x1}%+§[713)) : 2qu+%)(72%)\$§73’?11337 . 3° 3(3,2)=5;,3/1,aldy=§~7d7 3" éyi‘t km) a. .. . 1.. UR. 32¢ - 2737. g {3x13x172 \$9 + Mn) =1x3+k(%)=2x;=)l19)=6 mreion C? (lel'e) : 3x+2}1y% -iy L+ L SOFA? rim-a2; = (Mo/210) - (90,011) : —:—3 =-5 3 pts. 3. Compute the surface integral I = HfzdS for the surface S = {(x,y,z) : x2 + y2 = 1,0 S 2 51,): 2 0]. S Qc‘ ‘ _ I i 9 1' me 5. @{e,2)-( rose} 51n6,€3l“%5952)0525( '—' R :- \ £6? %2 SAT-1hth fat-aneﬁi‘i'aﬁon (F a C3 hide!- Sga SW“? 1713 it I; 1 .. \ “2'45 (056%.[dade _j(osgag. 5 '72. o 4% D ‘ Ty” V VI. 3 v I. ‘— ‘2. (l—s.n‘9)cmeae= jfmwae~ig srn’ecasede ‘1‘ a?» "I. . V a I - a “ 231“9W1"%Sin®{.y = im-fm-J'Ji '3 1. 1. 4pts. 4. Evaluate the surface integral I: ﬂ(x+y)2dS whereSis the part of the cone 22 = x2 +y2, betweenthe . S ‘ '3 'I._ al— 1'9 1' a} :it 13181165223 and 2:5. LQ‘t X '2 21:09) y:2S:n6)2:2-) x+7 _ (05 1.2. SM 9 éﬂ’ﬁﬂ) = (2(056123fne, 2)) 0595253 3 s 255 1T :‘a—QZ -25” 210560) 1‘ J K 99 3% Z '06-) J ‘ﬁ‘: Jayne, ice-se- o : {20353559 _2.) T? 2% g; = (we) sme, \> we me I ’ “ﬁn =W: ﬁe S 2. 21? 5 L §{X+9)°‘5:j\ f(9€o\$6+25{n9) U'iedzae 0 3 113' 5'3 : ‘33 I j& (|+(os&S:&8)d2-ul9 O 3 311’ S = r2; (\+cOSGSaR6)de - 5 2:12 0 3 2r: 5 I a” 4-1 1 t H '1. 2C0563b 2 2 A L‘. : ED‘HOD [ 6—245”%) = \I—l-Jrr- 3;“: = 272E? ...
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## This note was uploaded on 02/24/2011 for the course MATH 200 taught by Professor Jamesdcampbell during the Spring '10 term at Santa Barbara City.

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QUIZ 12 - Quiz 12 Sections 16.3-16.4(15 points Math 200...

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