Key_Quizzes_10_14

Key_Quizzes_10_14 - ; I "7(a) 4+ : ,2 + flangib...

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Unformatted text preview: ; I "7(a) 4+ : ,2 + flangib #5314117! : 16% f7 Me; 33%} M Jr gob}: 5”? f 3‘” 29%; Sm2+d7t; figmogg/ I) 2. Evaluate the line integral /C F - dr, where F : (332% —:By) and the curve C’ is given by the vector—function r(t) : (t3, t4), 0 S t S 1. 7W?» <66??? 4 - wkthWWN/w v 1 WWW, _ WWW/my «wwwnafi / _ 2 3 J (1% 0’7: f gem)???» Mfiée’z— 475’ C o mm w» we ,a WWW. MNM- muwwnwamwmvwwmhmxm wawmwwm “w, MATH ction 502, QUIZ #11 Name ............ Solve the following problems. Show the whole work. 1. (5 pts) Use Green’s Theorem to evaluate the integral f0 my d2: + y5 dy along the positiyelyw“xx oriented bondary of the triangle with vertices (0,0), (2,0), and (2,1). {\x " _ ,EManimmigrate 2. (5 pts) Use Green’s Theorem to evaluate the integral fC(y + efi)dm + (22: + cos yg) dy along the positively oriented boundary of the region enclosed by the parabolas y = 332 and m : y2. (W):- a We? evilé}; WW WNWWW-e WWWWW WW * W” W“ “WWMWWWWMV““\WmuuawwwmW‘ . , Mmewwmnmmw.» I v V‘x a t . r (l (9’39" law MAE» mmgfl éxa/ Ci X Z. ‘ M /Z . ‘46} _/ Name .................... Solve the following problems. Show the whole work. 1. pts) Given the vector field F : (yz, asz, my), find: (a) the divergence; (b) the curl am 11:23; (hug—MNng z 0 + 0 iii MWXWWW gm”?an * a a w 5) We NF; 9% i, L 1: th—x>rJQ—j)+z(§:g)=o,¢ flywho W.” 2. (%pts) Determine whether the vector field F : (yz,y2 + 232,3;y) is conservative. If it is conservative, find f such that F 2 V f . CAM MW Cur/ ESE? WW (‘jfé- L(x «LL; (‘7——)>+ 1294): E5) £7 a; . Conserretve, Solve the following problems. Show the whole work. 1. (10 pts) Write a parameterization for the part of the sphere m2 +y2 +22 2 4 which lies outside the cylinder 902 + y2 = 1. Make a sketch of the surface in question. Hint: You could use cylindrical or spherical coordinates. The most importnat part of the problem is to specify the parameter domain. wfl ' x ' _ .y flue/rm? CEWW‘éé’MfiMéS ‘ «A WflwwwwwmmmwwmwvaW»Wmm “Mir” 2/ u; 7%“ (liar/{7L5 mg ‘ a 2 , f; /':2«:;m Mai/54933 ( vie) 9W4 ’ r i- r 9 ' m ‘ . , r9 Mam féW‘f“ 4“») A4‘%m 7&9 74LWV/ . , (“mm WWAwmvwamwfiszmmwwwwww ,ggyyzagwfim V5 gag“ Eglfié [f3 ' § Z 2" , r. :2. / >< “l‘fml X3724??? 4% =2” $35 1 czj MATH 251 . 502, QUIZ #14 Name ......... Solve the following problems. Show the whole work. 1. (10 pts) Evaluate the surface integral F ' ndS, where F = (*m, —y, zz) and S is the part 5' of the cone z = V322 + y2 between the planes 2 = 1 and z = 2 with upward orientation. [éiél 43/ V Kiwi é ‘3:- [A V XV“: “W: .‘ V <mw W34} ‘ Z SSzweé +5413 i3? Jil‘t’ve av 7%}, MM?” mo WM pram/"4*" y, , ‘oété' 43 m Mr awat’éw/Vfié/S ®~ aéyéfljflg 3 ‘ $3221) Wyn—#6? 3‘: ) r3 T? “WW OéV—ézt yaWS‘nV 33$ 4.4ué2} {’= W ‘37 . Y‘: ChV ,3; .3, a!) 4 ) ’ QXQ=<~Mab\f)-M§mv) 147 Vy=<~u$;nv) New, 0? \JW “$55519 3‘ géuwflm) “z)'< “WWW s o?) 1 2 W W 3 ; M u g (u 0v}er uzamzcrw )’M J 1] (a $ liq—“.2 O r 31v :A(%+21> ~2T(3 4 34 6 ...
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Key_Quizzes_10_14 - ; I &amp;quot;7(a) 4+ : ,2 + flangib...

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