Math220-Sum11-Exam1v2-Solutions

Math220-Sum11-Exam1v2-Solutions - Mat 1 1 Exam l-June 30, r...

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Unformatted text preview: Mat 1 1 Exam l-June 30, r v N 7 Page 1 of2 Name: 50 [UJWDV’S Signature: Math 220: Multi—Variable Calculus Exam 1— Thursday, June 30, 2011 Instructions: 1. Clearly print your name and Sign your name in the space above. 2. There are 5 problems, each worth a specified number of points, for a total of 45 points. 3. Please work each problem in the space provided. Extra space is available on the back of each exam sheet. Clearly, identify the problem for which the space is required when using the backs of sheets. 4. Show all calculations and display answers clearly. Unjustified answers will receive no credit. 5. Write neatly and legibly. Cross out any work that you do not wish to be considered for grading. 6. Calculators may be used. However, all derivatives and integrals are to be found by learned methods of calculus. 7. The following table is strictly for grading purposes. Please do not mark. 8. Don’t quit until the time is up. Use all the time you have to keep trying. The following boxes are strictly for grading purposes. Please do not mark. ge 2 of 2 Math 220-9809, Summer 2011 Exam 1-June 30,11 1. Write the equation of the plane: (a) Passing thorough P0(1, 2, 3) and parallel to 3x — 2y+ 4z —— 5 = O . lle'C V =36~2§4¢W§ 13 Y‘OIMKKl 40440;; €le {Glam amcj '30 “PM. “(533 w’ch 3990W€~ The GQUO'LOH v04 [9/0146 (5 W11) «26/22) 4 M24) 2: 0 3X~ZV '5" 513:” (b) Passing through P0 (1, 2, 3) and 131(3.,—2, 1), and perpendicular to the plane 3x — 2y + 4z — 5 = O ! Hera B; a : 42/ '14] ~2> anal V;(3/ *2/47 are ' 5‘ ! yrs familial «Lo fl“- {eqmrcd {Pr-awe. “005) “.3 .‘ é ‘ NzPoFlXV:l: ~qwziz—20Cw—wlL/j-LQA gs ~2i—ll _. .5 I ' l ‘ A s ‘1 :32]! grill}, in {S a flow/m i “la “Wed *ff'ff‘fifl ” "C‘ 30/ -M‘f Q4” 6 ‘ “ll/ta Kim: 1's (Q'P0)'N: 'ZOCX‘IEI- 3“! (3%?)4QK2‘323 {2 3 ~99K$ £~£4V~§gm2q mg (0) Through 1330, 2, 3), P1(3,—2, l), and P2(5,0,—4). Ma 20-9809, Sumr2] Eam l-June , 2011 P 3 of 6 2. (a) Find the parametric equation for the tangent line to the helix with parametric equations x 2 cost, y = sint, z =t at the point (0,1,9. 2(e9=.4:,cws€, Srwéir“> Q3({) :— Z" wa‘é‘) (as?) "5 a Parana/r veclopk ‘(equt’mcl lame . TLg For‘mii' (0)1; Cafvrg Faint/3+0 {:(WZZ. (f'ékfjjl‘) 3'; 4 flflraflg/ Véffl'b‘f 4"“0 Yvé’qw‘f’i‘u l/me (0/1'/%)¢$o) éX/Y,2>:(0jl;W/7_74 X:-—~‘€ /, V: i/ 237%4'16 CW4 fit/ta Parmmalflc 455.35% Efét mm ‘33 . (b) Show that the triangle with vertices P(4,3,6) , Q(—2,0,8) , R(1,5,0) is a right triangle and find its area. ' " mg \ m #95,.” “’56) :2 wirmm ’ a} Pa2éwéng/2) awé’s' § r/ v”; “9/ a» "" lgwwiw Quail), Murr‘rfforc “NJ a“ ._.. r t, v kw We} ififiz P22? Pé’t‘Fcncll’wlav, Maw} m “"9 1 ; M1 1- 6mg lPéfxlanzlfyaggflZtamcé I mm 0‘( Warmiiéfaafigmm “etimteaf l9}! -:w:~ \) U‘ @WA PR, £0) arfcyk “— l A9612: 4,; E €53; m2 lémaigagm ii 2- E7 (c) Find the distance between the parallel planes x+y+z=5 and x+y+z=10 I flrgzl) wa mag—F an Atloijrmm” loatr’j’oin ”Haa fig/“Wat. XZl) iii/,6,“ g ['5 A FOUsr-Jzarx Tl/m Normal‘io X4'Y42'mm35’) {is Nflérlfjjjfpo TLM D-)i{i>ii(1)41(3)~mi ‘ an... Mt -- was...“ a...” .. w MW s w LL M " Page 4 of 6 Math 22009, Summer 2011 Exam une , Oll 3- (a) Find the curvature of the ellipse given by x = 3eost, y = 4sint, z = 0 at the point (0, 4, 0). 12“): Edged? + 5.1 gm; 4 {3} K @G):«y%4(14€majlnfl 12W): '7: (0566 « L1 63w" ‘3”er vi 6 J v\ »gg,p,{ (“HOS—4: 0 «the “New: Cl 1'? OCZl’OJ-l’ 12[Sim%‘l{flsw¥ K @H)XQYO=- '1 {2K 1 (2‘66) x (2%) l: :2 112%”) 5: Wqu (613715;) We}; 32 :54; (4%? +1 mm) ‘ i, ,, Tl»; Fw'anl {57/ MM?) (Wm; (9%»ng 71-5; {:2 30/ l/\(‘lT/Z).; 4/1 (b) Find the arc length for the curve given by R(t) = t i+ 300s tj + 3sint k , —5 S t S 5 . q . {Z (6): l c —3 anfj' + East/x 3 :2 \ WWWTWWWMW'WWWWW“L‘:.,~.1Mma.,wtmwm Ewmam 7 4 5 ll?— (f‘/[:\)124(w3$mf) 3,7; (53(03sz +43 (wig their) T % 672? 3 3 ‘3 r 5 L: lg (16) 14%:g Wale Wig :1 lama; —5 '5 "'5 th 22-99, mmer 201 W > WW W 7 PagS 6 Ba -June 02011 4.(a) A particle starts at the origin with initial velocity v(0) = i — j — 3k. Its acceleration is a(t) = 61 1+ 12t2 j — 6t k. Find the position function R(t). ” a , 3. V6021 5 aC-tficiwé: 31:26. “i” Hf J— 3152K Com‘éimn‘l’ 3”“(6 : CL'Kj‘“3‘/\\ (car‘s'iawi :: Cad—3K up ! iii 2 . - 72‘ N“ 50) Va): (affine er (wt 'iN +( 3f 3%? i i 3’ V (“/w NJ» QR): 3v“) (la; (£3415); +(f”v»{)d+z§—~£ 3‘6)*~4 "t i s4 Sew 2(0): aci-l ojlow (My-FL (leash:in m Oiiogj‘ioK. (b) Find the velocity, acceleration and speed of a particle with R(t) = 2cost i+ 3t j + ZSint k as its position function. v a) -.-. M) = («m e, a, m; Ea) : 2%) =1 Z-zang a, 45m) \V (%)l :. legit; 50.5% :2 M3 l; Speecl - 5. (a) Determine whether the planes x + 2y + ZZ = 1, and 2x —- y — 2z — 1 = 0 are parallel, perpendicular or neither. If neither, find the angle between them. Tim (Narmaleam Ni: (32/ Z 7 6mg; N2: [Z/‘Jl'2> TLe W0fmai5 Ara rig/l paraglei) go nel’le/ arc {la MS, Moreover), 'A/z 3'»le 7(0) $5: flight; 5' E , l l' a p gag ©6JCIA lo)’ (b) Consider the two vectors A = (x, 1, x) , B = (x, 2, 4). For which value(s) of x are the two vectors rth l?P 111? l' 1 th? e o ogona ara e or equa" 1n eng 660+ a I, V! a x o Cit/1A CHE. 01""l Lflrjgrgl \N\ncn “l heirfi Pvflciac‘é‘ ‘5 26m. ' é’WC’E W€V€f laszac We“ fire” mil/gr Al V’lnél {A $554., law 6:, flaring vi C 9 “if {(7 w? a: 3;” it???“ W1 $th t 6% J V; i in xiv x» )5 :2 l B) ...
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This note was uploaded on 09/13/2011 for the course MATH 20C taught by Professor Helton during the Summer '08 term at UCSD.

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Math220-Sum11-Exam1v2-Solutions - Mat 1 1 Exam l-June 30, r...

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