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# S 17-1 - Math 200 Spring 2010 Worksheet#28 Name_Ke_7...

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Unformatted text preview: Math 200, Spring 2010 Worksheet #28 Name _Ke_7________ Section 17-1 Green’s Theorem 1. Evaluate the line integral (:(ny dx+ x2 dy , where C is the rectangle with vertices (0, 0) ,(3, 0),(3,1) , and (0,1). ‘1 ﬁxydxﬁhr * (€330) MW "‘ 2. Evaluate the line integral (ijz + 323)dl7c+3xy2 dy,where Cisasshown. 3. ‘3 2 a. éhH‘y )clx-l- 3xy dy 3' éfgﬁxyvvﬁu +7389”) : 3 1— '1' AR : O (3)7( ) 3}) note. ‘Hm't E :' <x1+713xy1> \‘s ConSﬁvm’x‘Vf-l I 33)} (x1), ): 37": J31?) g; (77 "esmKJ‘le (\5X‘Slh (yq+<g)))dy - A i 0" Jule 0H. - %§[3X(15X'\$In[y3+3y)_,§ (””93 Y)}dn cry}: .0 CH7) 2?“ "7)” '2 33-” = “Tr-31] WM 0 4. Use Green’s Theorem to evaluate LF- ds where F(x, y) =( y2 eesx,x2 +2 y sin x) and C is the triangleﬁ'om( 0,)0 to( (,26) to (,)20 to 0.0 s (:59) §“ 1: a: : ~ 5((7 cosx)dx+ (X21) smx)d‘l 1 "“53; [NJ X +1y5lnX)';y(yC0Sx):)GlA we?» 0 endow 1, C ,5 : “Mllosxé 2 074; 53,} (ﬂ (2x:l7mx ”2750”) WA ‘1yj:2:dydx C ‘3 “Queues clockwise _ __ y- -3ch 5° “C glues +Ke Pom-{o9 one-him“ (5)0234:th :15?xe ~ ‘ngL .: ~l6 5. A particle starts at the point (—10,0) , moves along the x—axis to (10,0) , then along the semicircle y = 100—x2 to the starting point. Use Green’s Theorem to ﬁnd the work done on this particle by the force ﬁeld F(x,y) = —y2i+(y—x2)j. 1° to : 5;ng z [“7l0lx+(7~le:lx :gjl—aaxzrrxxl dill-'71)] a9 =gf01z+lylcm :0 TVS? {Ma-lav] _ 11‘ Coercitm-l-QJ ' 1; j("TCOSe +r9xh 6) rdrd 9 0 0 ‘ 1T [0 _ ”(we ~cose)cle- 5 r10” 0 1 ~ __ _ TI” lb :3 ID 2 l: («9. fungi, . "g T d : 20+n‘gép: 14.20:: 6. Which of the following vector ﬁelds are irrotational? If these were velocity ﬁelds of a ﬂuid, in Which would a small paddle wheel rotate, and if so, in which direction? Q Small PaJJk: soled chi y rol‘ql'e Cochlerclmkmlse. y Pal-ccl‘e. Clockwise (A) F = (_y9 I) curlz(F) = 2 Y‘O‘l'd'ev Clot wam, (C) F=(.V,0) (D) F=(y,x) curlz(F) = —l curlzdi‘) = 0 Show \$10M FIGURE 9 x2 2 7. Find the area enclosed by the ellipse 7a ———+12— = PWQmei-nie +he 9“me Let X“: qccst ) :: .Qr'sﬁn't ) 0.5-wa dX : .. QSI'n'td’c d? -'-' “£1105th _ _L 211* Arm ' :2 f“)! ~yc1>< : 3% a Cost {hostﬁlt * QJSIQ13("“\$‘-“J‘)‘Jt 0 2n- qﬂr . (Lg: : .. T ((0511: i‘Smx'iILJ't : :2 Q]? Tragi— o 8' If F(x,y) = (‘ny-W (x2 +y2) , Show that CLF - ds = 2:: for every positively oriented simple closed path that encloses the origin. ' ' . . . Since C 1.5 cm. avioi'i‘mr-g LiOSQoL PR'Hx ‘H‘Q'L' PhCJDSQS 'er 0513i; V i‘i‘ia dl..'¥'FL‘CUi+ +0 Campu'i‘e. ‘Hae Inn-e l“+93ﬂ.ld.\1‘eo+ig. Sciei" Cens'wler- 6.. COUn+2r-c{0ck‘uoise orieii'eal Cumbe C wrl'A (end-er 'HM. origin and max“ ct) where o. is Small enough“ ‘H'mi C i195 “RSI-\$9 C. Let 0 loo-Hue vagina bounded by C amelC’. “en 30 '-'- C U -C.’) 50 by Green's 'T'txenrem) ) Edei—Qéy + £7W/ " £7fo 3‘; AA :ff{i¥1 D “radiate Epcixﬁ-er :gﬂx‘f‘aci? ‘quqme'ihl’ec .‘ C(‘U'—‘(C«(65‘t GSiivs't')) O‘t-E 2W cu} L‘(as:d,a(ast) 2E __. , -; S F(Cf+))°2(1‘)dt :jQKh-‘Q5|K't)(‘ﬁ>nifii)+(&f03t)awsq o + 217 0; {0511: CL: Sugi; :: 5st -‘- Do 0 ~x xnmx Lian :0 [\$13 zfcf-a: Homework #29 Reread Section 17.1 {Due 05/05) Do Section 17.1 Exercises: 1, 4, 5 , 9, ll, 13, 15, 20, 22, 25, 27 Prepare for next class session: Read Section 17.2 ...
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