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Sol-261E1-S00

# Sol-261E1-S00 - MA 261 Exam 1 Spring 2000 Page 1/9 NAME...

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Unformatted text preview: MA 261 Exam 1 Spring 2000 Page 1/9 NAME ASL/L Till m STUDENT ID # RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1) Fill in the above information. Also write your name at the top of each page of the exam. 2) The test has 9 pages, including this one. 3) Problems 1 through 6 are multiple choice; circle the correct answer. 4) Problems 7 through 10 are problems to be worked out. Write your answer in the box provided. YOU MUST SHOW SUFFICIENT WORK TO JUSTIFY YOUR ANSWERS. CORRECT ANSWERS WITH INCONSISTENT WORK MAY NOT RECEIVE CREDIT. 5) Points for each problem are given in parenthesis in the left margin. 6) No books, notes, or calculators may be used on this test. Page 2 / 20 Page 3 / 20 Page 4 /10 Page 5 / 10 Page 6 / 10 Page 7 / 10 Page 8 / 10 Page 9 / 10 TOTAL / 100 MA 261 Exam 1 Spring 2000 Name: Page 2/9 (10) 1) Parametric equations for the line that contains the point (1, —2, 3) and is perpendicular to the plane 333 — 431 + 2z : 8 are: @\$:1+3t, y2—2—4t, z=3+2t B. \$:3+t, yz—4-l—2t, z=2+3t C. m=8+3t, 3428—415, z=8+2t D. \$:—1+3t, y=2—4t, zz—3+2t E. :Ez—l—3t, y=2+4t, 22—3—27? ﬁhﬁn'ﬂf%3)h~q_§ Divechon f 3f"? +02}? X=i+3c : —.;L~\$’7f’ ‘2, t: 3+9xt- “ 2 2 (10) 2) iim 31M ~ +2 ise ualto: (asthma) (\$2M?) (y ) q n A 0 B. 1 Aw SLi/@+19L) : @2 A D. 4 E LAX/we? (0H m 3‘ . Does not exist. ELL/M SEVNCXli’El) ,, Ali/V” (3+1): (XI g1)“(0/U) X“: 5L 7— ‘KX; yHom ) I'LO+®::; MA 261 Exam 1 Spring 2000 Name: ___—__— Page 3/9 _._) _' (10) 3) Symmetric equations for the line tangent to the curve r(t) : 1521' + (3t — 4)j + (2 — t2)k at the point (4, 2, —2) are given by: £1: %(3§~:‘1_:Q— B x=4andy—_—2:Z:2 ‘61: ~' ______ 3t :é C. x24zy+32:z—42 t: ' ‘ Z2 (10) 4) Let S be the level surface of f(x,y, z) 2 3:2 - y2 — Z corresponding to c : 1. The intersection of S with the my plane is: ,t p ‘2 7. 0 X l- g '2’?- —/ “l’ 2 :0 L S! a X 7:- #1 :— / two lines A. B. a circle C. a parabola D. an ellipse O a hyperbola MA 261 Exam 1 Spring 2000 Name: —) —> 5) An object has acceleration a(t) 2 67+ 21?, initial velocity v( ) : —> r(0) : 2;. Find the position vector of the object at time t = 1. art/=6 1+ .4 .2, -———§ -ma. «4) ﬁ‘fty5’0f57bc __2> 503:0 a i W) = eff + 1th .5; ., ~> 3:) HQ)? {619+ tlkigd , i=9 So szm:k {“7 _3,_ '4‘ “’7 x a~~k 4 Page 4/9 2', and initial position A. (e—iﬁ— 2J4]? (e — 1)i+ 2311— I? C. e;- 2; D. 65+ 2j+ I? a E. 65+ 25'— k MA 261 Exam 1 Spring 2000 Name: Page 5/9 (10) 6) Let f(;1:, y)_ — 011I1(:E2 + yz) with :c— — g(t ) and y = h(t ) Assuming that g(0) : 1, MO) =3, g’( ):2, and h’(() )=4, the value ofi(f(g(t), h(t)) whentins: I . A. g T -0 _44 /4{4 B a 1£;(/(I.II‘)444 40y 4 O ' g 7.; ._ .462 4' :ﬂ’f ' 474 . Z Tia/05) “5? 0,3) § f4 E. — 5 ‘1’ .31., A + .L 4/ Io [O MA 261 Exam 1 Spring 2000 Name: Page 6/9 i F”). P3 i e 7. Consider the plane containing the points (0,1,2), (1, 2, 3, and (2,1,0). (5) a) Find a vector 73’ which is perpendicular to the plane. (Put your answer in the box below.) .. ‘4 -—\ .1 »- 4 q q M.— Rpgfx RE: 'zkk—réfldjx (aircrew ~—-3l A ~y .. ’4 ~ k J l; :2” -;)§f{~-;~g7) +/< ~37) " I l- —} ,—> "9 Answer to 7a) ﬁ= ~02? +4: ‘— 917? (5) b) Find the equation for the plane. ”160-0) + [My-4) ~2(2 —:2) =0 - 1x + 4151 ~11; -—-4+ #20 —-— ')< + asp E :O Answerto7.b) ,__>< 7L 1%., 2‘ :Cl MA 261 Exam 1 Spring 2000 Name: Page 7/9 8. Consider the curve given by: —) '7'(t) = t2?+ 2tf+ (lnt)E, 13 t g e. (6) a) Write down an integral that gives the arclength L of this curve (including limits of integration). //f’0:)// ‘-' ﬂit: + 9073+ f:// L:/Q} ‘ ”t 1+ Z/HJQ‘Z Answer to 8.a) (4 )b )eComput the integral in 8. a) )to get the exact value of the arclength L. +44? 9114-! :- /;lf+1/ 6 * FH 91 Mt1+4+ﬁd2€ {e (3%“)th Q WHO/1" -. / 11w M62]_1"-::~(;e +1/ _ (s2) Answer to 8.b) L: 38.. l Page 8/9 XlefgC3 +JX3Q MA 261 Exam 1 Spring 2000 Name: 9. Let f(:1:,y) : 1:26”. (6) a) Find 38:5; , SL— : 7:3 Ex (I?! 4 y _ 1 ., , -, 9L; ‘ a L 1: .3 x01 6% 3 ML 3L 9?; cl X Answer to 9.21) 55:53] : (92 _ 7 (4) b) What IS 31:83] at the p01nt (1,0). 3% -~~-Ci )0) tech +0) gx;4 ~ Answer to 9.1)) 82f ﬁxay (1,0) = 3 MA 261 Exam 1 Spring 2000 Name: Page 9/9 10. A function f(;z:,y) is positive if y > 2, negative if y < 2. The graph of f is a plane which intersects the my plane at a 45*degree angle. % ?\ , (3) a) 3—5” W’ 1009.320 a n x L/zﬁix'“ 31 M— K 10- WtQQj "’ O 3f Answer to 10a) am, 2) : O 29 : pix-12\$) 2 =SI+9x 7V: 0 Answer to 10. b) 8f . 8—150 2):1 (4) c) Find the directional derivative of f at (0 2) in the direction t—J. .4“ . .21_ -__J Li— ."0 _ 0’1]... _,_l__ Bah/a) .- 01b?) a Answer to 10.0) J_ FD: ...
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