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Purdue MA 26100 - 261E1-F1998

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MA 261 EXAM I Fall 1998 Page 1/6NAMESTUDENT ID #INSTRUCTORINSTRUCTIONS1. There are 6 different test pages (including this cover page). Make sure you have acomplete test.2. Fill in the above items in print. I.D.# is your 9 digit ID (probably your social securitynumber). 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 ofthe pages of this test booklet. Circle your answers in this test booklet for the first 7questions. 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. Usinga#2pencil, 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 littlecircles.(b) On the bottom left side, under SECTION, write in your division and sectionnumber and fill in the little circles. (For example, for division 9 section 1, write0901. For example, for division 38 section 2, write 3802).(c) On the bottom, under STUDENT IDENTIFICATION NUMBER, write in yourstudent ID number, and fill in the little circles.(d) Using a #2 pencil, put your answers to questions 1–7 on your answer sheet byfilling in the circle of the letter of your response. Double check that you have filledin 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 andyour test booklet toyour instructor.MA 261 EXAM I Fall 1998 Name: Page 2/61. The set of all points whose coordinates satisfy the equationx2+ y2+ z2+6x +8y − 4z +4=0isA. a sphere with center (3, 4, −2) and radius 25B. a sphere with center (3, 4, −2) and radius 5C. a sphere with center (−3, −4, 2) and radius√33D. a sphere with center (−3, −4, 2) and radius 5E. None of the above2. Find parametric equations of the line that is perpendicular to the planeP :2x +3y − z =8and passes through the point intersection of P with the x-axis.A. x =4+2t, y =3t, z = −tB. x =2+4t, y =3+t, z = −1 −tC. x =4− 2t, y = −3t, z = −tD. x =2t, y =3t. z = −tE. x =4+2t, y =83+3t, z = −8−tMA 261 EXAM I Fall 1998 Name: Page 3/63. The curve traced out by the vector-valued function~F (t)=t~j +(1− t2)~k, −1 ≤ t ≤ 1is part ofA. a circle in the xz-plane starting at(0, −1, 0) and ending at (0, 1, 0)B. a parabola in the yz-plane starting at(0, −1, 0) and ending at (0, 1, 0)C. an ellipse in thr yz-plane goingthrough the point (0, 0, 1)D. a circle in the yz-plane goingthrough the point (0, 0, 1)E. a hyperbola in the yz-plane startingat (0, −1, 0) and ending at (0, 1, 0)4. Compute the length of the curve~r(t)=t33~i + t2~j +~k, 0 ≤ t ≤√5A.193B.53/2− 83C. 3D. 53/2E.53/2− 13MA 261 EXAM I Fall 1998 Name: Page 4/65. Find the unit tangent vector to the curve ~r(t)=2t2~i + t3~j +~k at the point (2, 1, 1).A.45~i −35jB. 3~i +4jC.45i +35jD. 4~i +3~jE.25~i +35j +15~k6. The level surfaces of the function f (x, y, z)=x2+3y2− 5z areA. elliptic cylindersB. elliptic paraboloidsC. hyperbolic paraboloidsD. elliptic hyperboloidsE. ellipsoidsMA 261 EXAM I Fall 1998 Name: Page 5/67. If f(x, y)=x2sin(xy) compute fyxA.B.C.D.E.8. Find an equation of the plane containing the points(2, 3, 1), (1, 1, 5) and (0, 1, 1).MA 261 EXAM I Fall 1998 Name: Page 6/69. A particle has acceleration ~a(t)=2~i + e+~j. The initial position is ~r(0) =~i +~k andthe initial velocity is ~v(0) =~j. Find the velocity ~v(t) and the position vector


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Purdue MA 26100 - 261E1-F1998

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