MAT318-QUIZ1 - MAT 318 Instructor: Mike Wang NAME: AN$WB£...

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Unformatted text preview: MAT 318 Instructor: Mike Wang NAME: AN$WB£ 10/19/06 Quiz # 1 Show all your work clearly! If you finish early, don’t forget to check your work. 1. Find the plane through (2,1,3), (4,4,5), and (1,6,0). (12 pts) “MM __9 P a P- Nm—E: Pa -_= <2.,3,2> , P72; <—\,s,-3> __;’w __> '3 ’1 ‘ L 7. Z 3 1761 >< PR : ‘ -l s ': “(LC—9140) —£(—Q+Q+£ 0MB) '7‘ ( I I - , £""”‘*P""°’ — <-\a,4/1%> ~ 662 OF PLANE: Mx—x.) + 1903-12,.)4r ace—11..) = O ‘ -Ia (X-L) 4-403-04141—3): O ‘(4X+Q‘Q_+‘$%:g 2. Evaluate the line integral IC 13/ ds, where C is the line segment joining (—1, 1) to (2,3). (12pm) More a ' \ a '9 o 4 c - rL-b3-C'Ur,+tn, -t-\ =Cl-t)<—\,i>++:<z,=s> = <-\ Wat, \'\’?_":> M M XL-H ‘6,Lt) +14 H .V ~ fl, £3Ll 9 L 3 2',"~‘s-3 "4-3 g ‘3; ‘ " A c1 HERE Ext: 3/ 33:4 .‘ S xa’ég —_ g xm'gkfl (jiffiaf a“: c, ‘ ‘— ____‘ 1: Q L—\ +3E)L\+LE)\131+7} 1 = Jab-Ht *ch gr. . 13 : ((7:14; +lz'kL-‘r 1431:5131" Pin] = “'2': 3. (22 pts) Given ?(x, y, z) = (ey, xey, (z + 1)ez), where sz:t2,y=t2,z=t3,0_<_t51. (i) Show that f is a conservative vector field. (6 pts) (ii) Find a function fsuch that F’ = Vf. (10 pts) (iii) Now use part (ii) to eveluate [C 1? 1d? along the given curve C. (6 pts) u) —’ _‘ ,t 2 E CURLF - 1 l 93% ax 8*} , H ‘1 "’ : LL 403-“ ~03 Jen/flu 0 L4,. F \s @HCEQ-Vfic'nVE "Cy : ‘0" £13: X99) IR}: Mr wax x ewes: R3453) -.- x244. 3(33\ 4 - -— '2 93 = Xe + game) 13.; -0 —> 05 LL09 Rxmx 1:3 = xe + Ma ' a t 5g} = k’gyzflgaa-ne Ag = Mac» = 9:2, UL L42. Qixwgru —. e + g5 +)& r \ \ , @013 'QUAM -§(o,o,o3 =09, «- l-e, +/)()—(o+o+/%\ QMUe/‘ : f 0 Y0“ '3 <°)\7)°> _ A 4 ’ ‘r(\)=<\,\,\> / 4. A particle starts at the point (—2,0), moves along the x—axis to (2,0), and then along the semicircle y = J4 — x2 to the starting point. Use Green’s Theorem to find the work done on this particle by the force field fix, y) = (x, x3 + 3xy1). (14 pts) ‘4- 2. a Kkflfzq of 3:4 WEE” z 2» 223* =>V=l M, ax ~3X *g‘g / 33*0 «/ USE Vodka :: [(gxl‘Fgg) * cookomares Extra Credit (5 pts) 2 Find the area enclosed by the ellipse 3% + y— = 1 MERE 0 9%: 5 ur a b2 ' “33?: PM“ 985 For. ELUPSE 1 X = OKCDS’C , t3: loscn‘t J dX : ~0k5€wkd4cIAa -.-: bans-t CH a: . . A : ax Avg -— lack x : figgatacosflcb Cos-k) — Lbscwtxsmscwfiél— \a 21‘: t 0": Sow“: twat) At ...
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This note was uploaded on 05/05/2008 for the course MATH 318 taught by Professor Wang during the Fall '06 term at Cal Poly Pomona.

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MAT318-QUIZ1 - MAT 318 Instructor: Mike Wang NAME: AN$WB£...

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