mid2sol - 2 dxdy. o y/3 2, ~')( 1. . ~ r...

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/ Mid-term Two i\lath 20E Section B. Winter 2011 UCSD I~VlSwer Name: ID Number: Section: Instructions: • NO CALCULATOR. • CLOSED BOOK. CLOSED NOTES, ('xcept for the formula sheet attached. • ID WILL BE CHECKED. GET IT READY! SHOW ALL YOUR WORK! (Final answer without. showing steps only earns partial cred- its. ) 1. (20 points) Let C(t) = (t, vT=t2) wit.h 0 S t S ~. Find the arc length. C'rt): ( I I {U-t'" r~ ) t ~ te-5 (9 \A~ \ J ~-ttQ-t ~ -{ J·t L \: ........ ,. " - l'Pu rt- 2r-f lU\. ~ * '- \ r c.l9 ~ r 1 ., \TV"" -~ L - ~ . ..1 L. 1
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2. (20 points) Let F = 3x 2 yi + (.£:3 + y3)j, a) compute curl F, and V' . F b) find a function f such that F ~ V' f. (A) (U'(t r:: ) ~ { ;- J '- .f. . '2 l:>'f. . ()I( CIt :: 01-\-0j t ~X -3x ., 7.y ~, )'f. . Y. -tV 0 ~ . t :: -h Ox 11) t- ; V (:t \y »)" 6 X Y t-? y l h) 11 f=qf,~fx:o)/r -fy~yJtyJ ), Iwt -[::: x 3 y + ~ Y If ~ e : {l ~ "'f\,O -t LlVl.,; ~ u.c 3. (2U points) Find the integral of 1 61,2 eX
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Unformatted text preview: 2 dxdy. o y/3 2, ~')( 1. . ~ r (-e"l-d. 1 Jx ) 0 ) 0 1 L jx ::: \ .Q.'f. . ~ Y. .) J X ~ _1\ -r y~ J 'I 2--. b ). S 1< e 1. J)( ~ LF Xl. . J u. , 'l( -I: + e U du. 2 ~ )r:::. 0 ~ L I<d X 2 ~ ~ "-~ -/:e 4/i> :-1: (Q '-1 ) 4. (20 points) Find the volume between the cone z = .JX2 + y2 and the paraboloid z = 1:2+y2. (Hint: You may use either double or triple integral. Use Change of coordinates if necessary.) -\. L 7 t:. tf'(liy1. =-l( +1 "\( L+yL=-1 1.';1 I 0-'1--= ~L r 1 r.,{:r:olrJ<9-> ) t r fY ( I t/ Z, )~ II ) ~ r ( r - r 2-) J r d Q /f. .. --.2T;. (+ r-3 4-I r ~ ) ! f ~t 5. (20 points) Evaluate Ie F ds where F = yi + 2:l'j + yk and the path c(t) = ti + t 2 j + t3k, O<;:t::;l. , jr, r cis = ~ ('/, t i 1. "I ~tI ). t.'( f) J.;t -.. C ({l., It,--{l.-). C I, Yf,1t'I.H. ))' ~ \.. +q.i-L + "3 1:'1-J;;t -( f i ) + .~ i: r ) ~ 54-15 3...
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This note was uploaded on 08/11/2011 for the course MATH 20E taught by Professor Enright during the Spring '07 term at UCSD.

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mid2sol - 2 dxdy. o y/3 2, ~')( 1. . ~ r...

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