261E1-S02 - MA 261 EXAM I Spring 2002 Page 1/6 NAME STUDENT...

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Unformatted text preview: MA 261 EXAM I Spring 2002 Page 1/6 NAME 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. You need to show your work. Circle your answers in this test booklet for the first 10 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. ((1) Using a #2 pencil, put your answers to questions 1—10 on your answer sheet by filling in the circle of the letterlof 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 Ad your test booklet to your instructor. MA 261 1. The angle between the vectors If = 2;- f-i- 2]}; and 3 = 2. The area. of the triangle with vertices (3, —2, 1), (7, —3, 4) and (5, 1, 0) is: EXAM I Spring 2002 Name: _‘ E —}is: A) 3J1?) C) fix/f; D) 9 E) 12 Page 2/6 MA 261 EXAM I Spring 2002 Name: —._.. Page 3/6 3. If P = (3, —~1, 2) and Q = (7, 1,6), the vector projection of I32) onto 2; is: A) 23‘ B) 32‘ C) 4? D) 53‘ E) 6? 4. The level curves of f(:r,y) = 832+”: ‘” are A. circles B. parabolas C. hyperbolas D. lines E. (noncircular) ellipses MA 261 EXAMI Spring 2002 Name: 4 4 5. Thelimit lim 9’ H is (mm—40,0) 2:2 + y2 equal to Page 4/6 A. 1 B. 0 C. 1/2 D. 2 E. Does not exist 6. An equation of the tangent plane to the graph of f(:c,y) = ‘fmz — 23; at the point where (2:, y) = (1, U) is A. a:+—y=1 B. $+y+z=1 C. m—y«—z=0 D. m-x/éy-z=\/§ E. y—z=1 MA 261 EXAM I Spring 2002 Name: 7. If msysz +m2yz3 = 2, use implicit differentiation to compute dz dz: pay-7.05:1? Page 5/6 — at (3:,y, z) = (l, 1, 1)- I NIH 8. Find a. vector function fit) which traces the curve of intersectiou of the surfaces y2+22=1andm=y 2 macaw.» fit) = (cost, sint, cos(t2)) fit) = (c032 t, cos t, sin t) fit) = (c0302), sin t, cos it) . fit) = (F, t, 1-432) W) = (32. m, t) MA 261 EXAM I Spring 2002 Name: _ Page 6/6 9. Al; what point do the curves intersect 93(3) = (3t, —3 + t, 1 + :3) 172(5) 2 (s + I, —s, s) in . (3,0,1) . (3,—3,0) . (6,—1,2) . (0,1,—1) . (3,—2,2) U: U0 {1] 10. Find parametric equations for the tangent line to the curve f-‘(t) = (t2 + 3t + 2, e‘ cost. 111(t + 1)) at. the point (2,1,0). A. ~.'-:=-2+3t, y=l+t, z=t . 1 B. a: =2t+3, y: e‘(cost—smt), z = m C. I=3+2t,y=1+t, z=1 D.:c=3t y=2t z=1+t E. m=1—t y=2+t z=2—3t ...
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