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Sol-261E1-F98

Sol-261E1-F98 - MA 261 EXAM I Fall 1998 Page 1/6 NAME E...

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Unformatted text preview: MA 261 EXAM I Fall 1998 Page 1/6 NAME E ULLT"C an S STUDENT ID # INSTRUCTOR INSTRUCTIONS 1. There are 6 different test pages (including this cover page). Make sure you have a complete test. 2. Fill in the above items in print. I.D.# is your 9 digit ID (probably your social security number). Also write your name at the top of pages 2—6. 3. Do any necessary work for each problem on the space provided or on the back of the pages of this test booklet. Circle your answers in this test booklet for the first 7 questions. Partial credit will be given for work on the last 3 questions. 4. No books, notes or calculators may be used on this exam. 5. Each problem is worth 10 points. The maximum possible score is 100 points. 6. Using a #2 pencil, fill in each of the following items on your answer sheet: (a) On the top left side, write your name (last name, first name), and fill in the little circles. (b) On the bottom left side, under SECTION, write in your division and section number and fill in the little circles. (For example, for division 9 section 1, write 0901. For example, for division 38 section 2, write 3802). (c) On the bottom, under STUDENT IDENTIFICATION NUMBER, write in your student ID number, and fill in the little circles. (d) Using a #2 pencil, put your answers to questions 1—7 on your answer sheet by filling in the circle of the letter of your response. Double check that you have filled in the circles you intended. If more than one circle is filled in for any question, your response will be considered incorrect. Use a #2 pencil. (e) Sign your answer sheet. 7. After you have finished the exam, hand in your answer sheet and your test booklet to your instructor. MA 261 EXAM I Fall 1998 Name: ___—_____ Page 2/6 1. The set of all points Whose coordinates satisfy the equation x2+y2+z2+6x+8y—4z+4=0 is A. a sphere with center (3, 4, —2) and radius 25 B. a sphere with center (3, 4, —2) and radius 5 C. a sphere with center (—3, —4, 2) and radius v33 ([9 a sphere with center (—3, —4, 2) and radius 5 Cm» if“? (dc if ETA“ 'VVVI: ’ i E. None of the above /-{V~L + C/ A. (5.3),. 894 AC}. ifl42 ”4* a " ‘7 +1 C3 "i" 4" —— 4L ' , , .A . V C m I! ’ . ”I 0+1) 4M~;~J+/ »/»r‘» 1" 2; c' . 2. Find parametric equations of the line that is perpendicular to the plane 77 : 2:1: + By — z = 8 and passes through the point of intersection of ’P with the x-axis. . :4 2t, :3, :- V‘*~.‘IH\§ (:‘uZ‘ ‘kl/IL lv’d Y;""(' "" .1: + y t z t B. x=2+4t, y=3+t, z=-1—t 1 t f': 4. 2. 6y»: : k: C. $24—2t,y:—3t,z:—t _... ,x “ ?X + _: ’3 -—(J I ’- D $=2t,y:3t.z=—t E. $=4+2t, y: 3+3t, z: —8—t (30,914,3'3) Ni « a; c! Mm”; at E ( “i ( in “I? i\‘ i— ”: {J —: I -+ L ”LL X:4~L'/T "t-ET '2: t MA 261 EXAMI Fall 1998 Name:_____ Page 3/6 3. ,The curve traced out by the vector-valued function 13(t) = 753+ (1 —t2)l'5, —1gtg 1 is part of Pa wax» (,l r -‘ c , "lam ,l 5 f t ‘ * l CUR ’A 3 A. a circle in the Luz-plane starting at X '2 Q ‘_ U :1: ,r {K :— _j__'tlL (0, —1,0) and ending at (0,1,0) Q I! a parabola in the yz—plane starting at X 3 Q I ‘2'? g1“ , C (0, —1,0) and ending at (0,1,0) 3?: :3.” ’l ,_ “‘2‘; C. an ellipse in the yz—plane going 4 H ‘ A 3‘ .: through the point (0,0, 1) :31“! a“ ”I l. h) —1 ) 1:} ,2 WM“ #12; a Circle in the gz-plane gomg ‘ ‘ Q ’ ’ through the pomt (0,0, 1) a mi" AL o it (77‘: l , Q) E. a hyperbola in the yz—plane starting at (0, —1,0) and ending at (0,1,0) 4. Compute the length of the curve 3 t ‘O —a -¢ F(t)=§i+t2j+k, Ogtgfi / \{ ' ‘\ "f ‘3 . «LL/l . (' Jr, a fl ‘1';— % t 3 ~-—--’ 5 l'—;r' ‘ ‘L t ‘4‘”: E 1": (_/\n 5 /2 — 1 L " 3 W“ N)“ at} A. —3 0 ‘ :7 53/2 _ I F“ *WW;§"““" ‘ ’ , L B 8 3: l {(1 l J“ 9‘5‘ + J ’ 3 J 0 C. 3 Cl yr: WW , D 53/2 { " ' r*~~X—- z 47'" x; l 19 ‘W \ .1” 1‘” L E. _ )0 ( «t 3 ', www.mwfl » - x 3 f ( \l "a l g A} * 3‘ § 1 ‘\ :4 yo J I 1 " J, i~~jx I L. if .. ‘ r (I \t “l" 4 ) (j _———-. i L3. + 4 x) L” A *' t ” /; 9 fl 1 5/ MA 261 EXAM I Fall 1998 Name: ___________ Page 4/6 5., Find the unit tangent vector to the curve F(t) = 2t23+ t3i+ I? at the point (2, 1,1). .‘ . ~ "”5 'ln“ 3....» M d 22 4. i 4 l(. :3 TLt ; +1 V + 24, A. fist-g] . it .33, 4:: L @§z+-:-a 1 :1 J D. 4H3} E. §E+§j+§i€ W i x ‘ J v \(r. (+).: 41‘ “T" «in c. .4 w .3"? ~~*/ MMMMMMM "W r‘ w full =W~ 7 N ‘If. ,... “A, W” K ‘J m 4“ L. '- U ”I -_ ”f ”“7““ ,_ '1: 4’” I; ‘ 1: x \l 6. The level surfaces of the function f (:17, y, z) = x2 + 3y2 — 52 are A. ellipsoids X + if x A“ w. - , 5 W ® paraboloids a . ‘ , C cones r' .- ‘ . i . 'A ’1_\ J‘ w \X .L- V _ f ,— ~: w (a D. spheres E. cylinders MA 261 EXAM I Fall 1998 Name: ___._—___ Page 5/6 7. Compute 565% if f(m,y) = m2 sinmy. A. 2m cos my — mzy sin my $015 :— X “Hwy ‘3‘ of 3m2 cosmy—m3ysinmy AA A? "A"; 1 0- 3m2 cos my —-—=-—-:: X C131x'-2\>( "3 Us A D. 2m cos my 0' j ‘X N {,0 g; \< a E. 2m cos my — m2 sin my 1: I -,, J E} + , FL w.~u‘.L--w»/~' ‘7‘: X ( .—— f.\ m :3! at.) . k4 +- 3 >( (:13 L X D ‘A ’x 73 ‘g! C K m :- " XA LA ”A 30;) + 33(1210‘ SI ~ 2 A B c 8. Find an equation of the plane containing the points (2, 3, 1), (1, 1, 5) and (0,1,1). ”“5 ”T. "_ ‘ 1... RES» :- «L -—-‘n‘:§ +4.“ ASIVAA :« “2‘; “(Ii—i ~~~~~~ fl '" '7 14 3 w M \ v) #9 ,W, q: “HM-aw} L A a»; $1 w (a 5 _ (J. k I 0 A g- l ' 4 1 MA 261 EXAM I Fall 1998 Name: ___________ Page 6/6 9. ,A particle has acceleration 5(t) 2 25+ 6‘}. The initial position is 77(0) = 27+ 1: and the initial velocity is 17(0) 2 j. Find the velocity 17 (t) and the position vector F(t). fl 31:2 + 227312 + y2 (a) What is the limit of f (50,34) as (13,31) approaches (0,0) along the x—axis. (b) What is the limit of f (13,31) as (17,31) approaches (0, 0) along the y-axis. (c) Does the lim(z,y)_,(0’0) f (x,y) exist? If yes what is its value? ...
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