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Unformatted text preview: umsxmvneaxmwmxxvflxwrim‘zWNW-5:»:xmmwWWAVwammWWamWWaWWWWWWWWWmfiMWAm&wwx’miaskxsn MATH 174 Quiz 9 Tuesday April 19 . . I , I Name. S.'u+.m Sectlon. PID. Solve the problem systematically and neatly and show all your work. 1. Let F 2 xi + yj and C be the circle: r(t) = (cost)i + (sin UL 013 t S 27r. (i) (2pts) Find the circulation of the field F around the circle 0. (ii) (2pts) Find the flux of the field F across the circle 0. £6 01va :JL’E.301/5: fcmabwwdy 6) 3Com ‘39 l: ‘3‘“ Q3 Mal/#A/dx ng my le mzaot 0‘)“ -SJ/‘T‘édl‘v 2. Let F = nyi + (x2 — 22)j — Zyzk, \\ . (1) (Zpts) Show that F IS conservatlve. (ii) (2pts) Find a potential function f (as, y, z) of F. 9 . iii 2 ts Evaluate - , '3 < up) (3,2,1) a; , L3 /0 nyda: + (a:2 — 22)dy — 2yzdz (2 1 0) , - I Z » F (/3 “WW" N’XL’EL I 2X X . , 4 , if“ L SE] szzl (DJ; mg :5 fcxjwwxlwcyg) :5 $3,)(4-g3n- 3%"3 5 363‘“"3% +5“) > JECXJ%):X:1 jéfi/iw) 5.3» :d)fl£—+AC%);—ujg :5 “”30 :5 Mafia 77W) [News fir/331+ c I {3; \ ® j‘ I) “J dx+€x£y>9lj’?9id% : .fc$.2,/)- fume) :[x'15+c)~«(¢+c) »/2 (21/ D) ...
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