CWA9e-FEAns_97_08 - 15 2 45 0.78 46 6 47 2 x sec 2 x 2 1 48...

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ANSWERS TO FINAL EXAMINATIONS 25 ANSWERS TO FINAL EXAMINATIONS FINAL EXAMINATION, FORM A 1. (7 . 5 , 157 . 5) 2. log 2 d = a 3. 4. 4 5. 5 6. 1 4 7. y ± =7 xe 3 x (2 + 3 x ) 8. y ± = x +1 x ln(3 x ) x ( x +1) 2 9. 14 10. y =8 x +9 11. 12 125 12. Increasing on ( −∞ , 2) and (6 , ); decreasing on (2 , 6) 13. Relative maximum of 1 at 2; relative minimum of 13 at 4 14. (a) ( −∞ , 0) and (2 , ) (b) (0 , 2) (c) (0 , 5) and (2 , 21) 15. ( x +4) e x 16. Absolute maximum of 0 at 0; absolute minimum of 16 at 2 17. 20,000 18. dy dx = 3 14 x 1 / 2 y 14 x 3 / 2 +30 x 1 / 2 y 2 19. 12 20. dy = 18 x ( 2+ x 2 ) 2 dx 21. 3 π in. 3 22. x 3 7 2 x 2 +2 x + C 23. 1 8 ln | x +9 | + C 24. 56 9 25. 1 2 ( e 4 1 ) 26. 10 10 3 10 . 54 27. e x ( x 2 2 x +2 ) + C 28. 3 4 ( 3 e 4 +1 ) 123 . 60 29. 39 30. 120 π 31. Converges; 1 32. 4
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26 ANSWERS TO FINAL EXAMINATIONS 33. (a) None (b) 3 at ( 2 , 2) (c) None 34. 5488 when x =14 and y =28 35. 0 . 12 36. 3 2 e 4 3 2 e 2 70 . 81 37. y 2 = x + e x + C 38. y = x 3 7 2 x 2 +2 x +4 39. y =4 x 2 3 x 3 +20 40. 0.5 41. (a) 3 2 (b) 0.75 (c) 0.866 42. 0.0668 43. (a) 1 3 x + 9 x 2 2 9 x 3 2 + 27 x 4 8 (b) 0.9704 44.
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Unformatted text preview: 15 2 45. 0.78 46. 6 47. 2 x sec 2 ( x 2 + 1 ) 48. x 2 sin x (3 sin x + 2 x cos x ) 49. 1 3 tan (3 x + 1) + C 50. 1 64 FINAL EXAMINATION, FORM B 1. (a) 2. (d) 3. (a) 4. (c) 5. (b) 6. (c) 7. (c) 8. (c) 9. (b) 10. (a) 11. (c) 12. (d) 13. (b) 14. (a) 15. (b) 16. (c) 17. (c) 18. (b) 19. (a) 20. (a) 21. (a) 22. (c) 23. (a) 24. (b) 25. (a) 26. (d) 27. (b) 28. (d) 29. (c) 30. (b) 31. (a) 32. (d) 33. (c) 34. (c) 35. (b) 36. (b) 37. (a) 38. (b) 39. (c) 40. (c) 41. (b) 42. (b) 43. (a) 44. (d) 45. (a) 46. (b) 47. (a) 48. (b) 49. (a) 50. (d) SOLUTIONS TO ALL EXERCISES...
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CWA9e-FEAns_97_08 - 15 2 45 0.78 46 6 47 2 x sec 2 x 2 1 48...

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