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Spring 2006 MTH 103: Answers to Even Problems LESSON 2 (12.2, p. 786): Vectors in R 3 18. comp a b = comp b a = - 11/ 14 42. perpendicular 62. cos - 1 (1/ 3 ) 68. x - y + 2z = 8 (plane through A and to n ) 70. α = cos - 1 ( - 1/3) LESSON 3 (12.3, p. 794): Cross product 30. 16 195 /195 LESSON 4 (12.4, p. 801): Lines and planes 14. x = 2 + 3t y= - 1+t -∞ < t < ; 2 1 5 3 1 1 x y z - + - = = - z = 5 - t 30. x + y - 2z = - 2 32. 15x - 9y - z = 16 40. π /2 56. (7 2 )/5 LESSON 5 (12.5, p. 813): Curves and motion in R 3 p. 813 2. Fig. 12.5.18 4. Fig. 12.5.15 46. α = π /4 64. (6 sin 15 ° ) 2 2.4115427 ft. ( Hint : See Example 10 in text.) p. 845 16. x + 2y + 3z = 6 LESSON 6 (12.6, p. 828): Curvature and acceleration 6. L = 2e - (1/e) - 1 10. κ = 2 /250 18. T = 1/ 13 [3 i – 2 j ], N = 1/ 13 [ - 2 i - 3 j ] 34. 4 2 4 2 3/2 2 9 9 1 (9 4 1) t t t t + + + + 42. T = 1/ 14 [ i +2 j + 3 k ], N = 1/ 266 [ - 11 i - 8 j + 9 k ] 54. κ = 8 2 /3; center of curvature is (21/16, 21/16) LESSON 7 (12.7, p. 837): Cylinders and surfaces 1

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30. ellipsoid with center at (0,0,0) LESSON 8 (13/2, p. 857; 13/3, p. 866): Functions of several variables; limits and continuity p. 857 54. 13.2.39 56. 13.2.40 58. 13.2.43 p. 866 24. does not exist 30. /2 LESSON 9 (13.4, p. 875): Partial derivatives 58. (a),(c) LESSON 10 (13.5, p. 886): Maximum-minimum 12. (0,0,0), (1,2,4/e), ( - 1,2, - 4/e), (1, - 2, - 4/e), ( - 1, - 2,4/e) 18. ( - 1,0, - 1) 24. 3 is the maximum value and - 1/4 is the minimum value 26. 2 is the maximum value and
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