# 261FE-S06 - MA 261 FINAL EXAM May 1 2006 Name Student I.D Lecturer Recitation Instructor Div — Sec Instructions 1 This exam contains 25 problems

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Unformatted text preview: MA 261 FINAL EXAM May 1, 2006 Name: Student I.D. #: Lecturer: Recitation Instructor: Div: — Sec: Instructions: 1. This exam contains 25 problems worth 8 points each. 2. Please supply a_ll information requested above and on the scantron. 3. Work only in the space provided, or on the backside of the pages. Mark your answers clearly on the scantron. Also circle your choice for each problem in this booklet. Make sure your test cover page and scantron are the same color. 4. No books, notes, or calculator, please. MA 261 FINAL EXAM SPRING 2006 1. Find the Volurne _‘of the parallelepiped with edges determined by the vectors 63=3i+2j+k,b=j+2k,andE=i—2j+k. A. 3 B. 6 C. 9 D. 18 E. 24 2. Find parametric equations for the line passing through P = (2,1,—1), and perpen- dicular to the plane 43: + 2y + 3z : 8. A. w=t+4,y=t,z=—t B. m=4t+2,y=2t+1,z=3t—1 ac—2__y—1 z+1 C. 2 9 —1 E. w=4t—2,y=2t—1,z=—3t+1 MA 261 FINAL EXAM SPRING 2006 3. Find the equation in spherical coordinates for 3:2 + y2 = :13. A. p = sin¢cos0 B. psinqb : sin2 qbcos6 C. p = sinqbcosqb D. p2 = pcos qb E. p2 sin2 ab = psinqbcosﬁ 4. Find symmetric equations for the line through the origin and perpendicular to the lines 03 y 2 L 52342—2 and 03:523. :1: z A'EZ—i723 a: 0.32%22 a: a: E-§=%=§ MA 261 FINAL EXAM SPRING 2006 5. A vector parallel to the tangent to the curve at = 3t%, y = 2t3 — 1, z = 1% at the point P(3, —3, 2) on the curve is: —22'+ 35'— 21? ~2€+ 33H]? —2E’+ 35+]? —2E'— 35'— 1? 45—33—21? ECQW? 6. The curve given parametrically by: 7r x=cos3t, y=3, z=sin3t, Ogtg E has arclength equal to: ?> EUQW MA 261 FINAL EXAM SPRING 2006 {E 7. Evaluate ffR 2fdA where R is the region bounded by the lines y = 5, y 2 ac, and between y = 2 and y = 4. A. 21n2 B. 121n2 8. If = emy 1n y, then fy(2,y) = MA 261 FINAL EXAM SPRING 2006 9. One vector perpendicular to the plane that is tangent to the surface 3:2 + 3/2 + z = 9 at the point (1,2,4) on the surface is: 2E+2E+E 2Z+4§+E —2Z—4§+E {+5—4E Z+i+4E spam.» 8 10. Suppose z = f(w,y), Where as = 6’3 and y : 2s + 3t + 2. Given that 6—: = 2533/ and 62 _ 2 a _ _ a—y-x ,ﬁndgfwhens—Oandt—O. MA 261 FINAL EXAM SPRING 2006 11. Find the direction in which the function z = m2 +3my — % y2 is increasing most rapidly at (—1,—1). 29 53+ 23' — I? —5Z—— 23' -o -o . 22' — 53' «29 \$60.06? 12. The function f (m, y) = 6m2 — 2m3 + y3 + 3y2 has how many critical points? A. None B. One C. Two D. Three E. More than three MA 261 FINAL EXAM SPRING 2006 13. If 77(t) = t2i+ 3155+ I? is the position of a moving particle at time t, then the speed of the particle at t = 1 is: 8.1 + 33+ I? . EUQW? [Q “l + me 14. Find the maximum value of \$2 + 3/2 subject to the constraint 1:2 — 2m + 3/2 — 4y : 0. A. 2 B. 4 C. 10 D. 16 E. 20 MA 261 FINAL EXAM SPRING 2006 15. Let R be the region in the xy—plane bounded by y = x, y := —:v and y 2 v4 — x2. Evaluate the integral // ydA. R A, ELVE 2 8 B. — 3J5 4 C. — ﬂ Sﬁ D. —— 3 E. 4\/§ 16. A lamina in the spy—plane bounded by y = 0, x = 0 and 2x +. y = 2 has mass density at (12,31) equal to the distance to the :raxis. Find the mass of the lamina. 1 A.— 3 2 B.— 3 4 C.— 3 D.2 E.1 MA 261 FINAL EXAM SPRING 2006 17. Find the surface area of the part of the surface 2 = 3:2 + 3/2 below the plane 2 = 9. 18. Find a, b such that A. ECh/g — 1) B. %(3\/§ — 2x5) C. 3&(373/2 — 1) D. 363(293/2 — 1) E. gar-3W2 — 1) 3 V9—m2 2 2 a b / f / zzzcdzdyda: = / f / zzzcdxdydz. 0 0 0 0 0 0 10 A. a=3 b=3: B. azm b=3 C. a=3 bzﬂ D. a=z b=3 E. a=3 bzm MA 261 FINAL EXAM —1 19. 11111 443+?) cos(:z:2 + yz) (w,y)—>(0,0) SPRING 2006 A. equals 0 B. equals —1 C. equals 1 D. equals 6— 1 E. does not exist 20. If F(m, y, z) = (a: sinm+ y)§'+ myj’jL (yz +3013, then curl F" evaluated at (7r, 0, 2) equals 11 A. muow 7r?—3+ I; ﬁ—j—ﬁ 2?—7r3+ I; 2;—;+7rlg ﬁ+j+k MA 261 FINAL EXAM SPRING 2006 21. Evaluate / (251: + y)d\$ + (Edy 0 Where C':F(t) = t2(1+ 05+ cos (gtz) 3—", 0 g t S 1. ECQW? CUO1H>NH 22. Consider the surface S:\$=u+v, y=u~v, z=u2+vz. Find the equation of the tangent plane to S at the point Where u = 1 and v = 0. A. 2\$+2y+z=5 B. \$+2y—z=0 C. 2\$+y—z=0 D. \$+y+z23 E. \$+y—z:1 12 MA 261 FINAL EXAM SPRING 2006 23. Evaluate + 3/2 + 22)dS Where S is the upper hemisphere of 11:2 + 3/2 + 22 = 2. S A. 27r B. 471' C. 57r D. 67r E. 87r 24. Evaluate / 4yda: + 2:1:dy Where C is the semi-circle 11:2 + 3/2 = 1, y 2 0 oriented counterclociwise. A. 0 B. 7r C. 27r D. —7r E. —27r 13 MA 261 FINAL EXAM SPRING 2006 25. Calculate the surface integral // 13" - 73 d3 Where S is the sphere x2 + 1/2 + 22 = 2 s oriented by the outward normal and 13(1), y, z) = 5x3§+ 5y33+ 5231;. 48\/§7r 167r 2471' 25\/§7r 2071' \$3.033? 14 ...
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## This note was uploaded on 04/09/2008 for the course MA 261 taught by Professor Stefanov during the Fall '08 term at Purdue University-West Lafayette.

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261FE-S06 - MA 261 FINAL EXAM May 1 2006 Name Student I.D Lecturer Recitation Instructor Div — Sec Instructions 1 This exam contains 25 problems

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