Section 14.3 AN99 12. ≈ ≈ ° ≈ ° a B C 6.09, 31.9 , 108.1 ; ≈ area 14.46 square units Cumulative Review (page 938) 1. { } − + i i 1 3 2 3 , 1 3 2 3 2. (22, 29) (25, 0) (0, 25) (1, 0) y 10 x 10 x 5 22 3. (21, 24) (22, 22) (0, 22) y 5 x 5 4. { } ≤ ≤ x x 3.99 4.01 or [ ] 3.99, 4.01 5. { } − + − − − i i 1 2 7 2 , 1 2 7 2 , 1 5 , 3 6. (1, 6) y 10 x 5 y 5 5 Domain: all real numbers Range: { } > y y 5 Horizontal asymptote: = y 5 7. 2 8. { } 8 3 9. = = − = x y z 2, 5, 3 10. 125; 700 11. y 3 x P CHAPTER 14 A Preview of Calculus: The Limit, Derivative, and Integral of a Function 14.1 Assess Your Understanding (page 944) 3. a 4. does not exist 5. T 6. F 7. 32 9. 1 11. 4 13. 2 15. 0 17. 3 19. 4 21. Does not exist 23. y x 5 15 ( ) = → f x lim 13 x 4 25. y x 5 5 ( ) = − → f x lim 3 x 2 27. y x 5 8 ( ) = →− f x lim 6 x 3 29. y 1.25 x P ( ) = π→ f x lim 1 x /2 31. y x 2.5 2.5 ( ) = → f x lim 1 x 0 33. y x 5 5 ( ) = − →− f x lim 1 x 1 35. y x 5 5 ( ) = → f x lim 0 x 0 37. y x 5 5 ( ) → f x lim doesnotexist. x 1 39. y x 5 5 ( ) = → f x lim 0 x 0 41. y x 5 5 ( ) = → f x lim 0 x 0 43. 0.67 45. 1.6 47. 0 49. d M 4 5; 4, 7 ( ) = = − 50. Center: 2, 1 ; foci: 2, 3 , 2, 1 ; vertices: 2, 13 1 , 2, 13 1 ( ) ( ) ( ) ( ) ( ) − − − − − 51. $7288.48 52. 4, 2 3 π ( ) 14.2 Assess Your Understanding (page 952) 3. product 4. A 5. b 6. T 7. F 8. F 9. 5 11. 4 13. −10 15. 8 17. 8 19. −1 21. 8 23. 3 25. −1 27. 32 29. 2 31. 7 6 33. 3 35. 0 37. 8 5 39. 0 41. 2 4 43. 5 45. 6 47. 0 49. 0 51. −1 53. 1 55. 3 4 57. y x 3 23 12 212 f(x) 5 x 3 1x 2 11 58. ( ) = − − −g x x x 3 2 1 59. ° 60 or π 3 60. + + + + x x x x 8 24 32 16 4 3 2 14.3 Assess Your Understanding (page 958) 7. one-sided 8. ( ) = → + f x R lim x c 9. continuous; c 10. F 11. T 12. T 13. { } − ≤ <− − < < < ≤ x x x x | 8 6 or 6 4 or 4 6 15. 8, 5, 3 − − − 17. ( ) ( ) − = − = f f 8 0; 4 2 19. ∞ 21. 2 23. 1 25. Limit exists; 0 27. No 29. Yes 31. No 33. 5 35. 7 37. 1 39. 4 41. − 2 3 43. 3 2 45. Continuous 47. Continuous 49. Not continuous 51. Not continuous 53. Not continuous 55. Continuous 57. Not continuous 59. Continuous 61. Continuous for all real numbers 63. Continuous for all real numbers 65. Continuous for all real numbers 67. Continuous for all real numbers except π = x k 2 , where k is an odd integer 69. Continuous for all real numbers except x 2 = − and = x 2 71. Continuous for all positive real numbers except = x 1 73. Discontinuous at = − x 1 and = x 1; R x lim 1 2 : hole at 1, 1 2 x 1 ( ) ( ) = → ( ) ( ) = −∞ = ∞ →− →− − + R x R x lim ; lim ; x x 1 1 vertical asymptote at = − x 1 75. Discontinuous at = − x 1 and = x 1; ( ) ( ) = − →− R x lim 1 2 : hole at 1, 1 2 x 1 ( ) ( ) = −∞ = ∞ → → − + R x R x lim ; lim ; x x 1 1 vertical asymptote at = x 1 y x 5 5 x 5 21 y 5 0 y x 5 5 x 5 1 y 5 1
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