Originating on Pentecost Island in the Pacific, the practice of a person jumping from a high place harnessed to a flexible attachment was introduced to western culture in 1979 by the Oxford University Dangerous Sport Club. One important parameter to know before attempting a bungee jump is the amount the cord will stretch at the 28. x3 + 2x2 - 3x 7 0 29. x4 7 x2 30. x4 6 9x2 31. x4 7 1 32. x3 7 1 33. x + 1 x - 1 7 0 34. x - 3 x + 1 7 0 35. 1x - 12 1x + 12 x 0 36. 1x - 32 1x + 22 x - 1 0 37. 1x - 222 x2 - 1 0 38. 1x + 522 x2 - 4 0 39. x + 4 x - 2 1 40. x + 2 x - 4 1 41. 3x - 5 x + 2 2 42. x - 4 2x + 4 1 43. 1 x - 2 6 2 3x - 9 44. 5 x - 3 7 3 x + 1 45. x2 13 + x2 1x + 42 1x + 52 1x - 12 0 46. x1x2 + 12 1x - 22 1x - 12 1x + 12 0 47. 13 - x23 12x + 12 x3 - 1 6 0 48. 12 - x23 13x - 22 x3 + 1 6 0 Mixed Practice In 4960, solve each inequality algebraically. 49. 1x + 12 1x - 32 1x - 52 7 0 50. 12x - 12 1x + 22 1x + 52 6 0 51. 7x - 4 -2x2 52. x2 + 3x 10 53. x + 1 x - 3 2 54. x - 1 x + 2 -2 55. 31x2 - 22 6 21x - 122 + x2 56. 1x - 32 1x + 22 6 x2 + 3x + 5 57. 6x - 5 6 6 x 58. x + 12 x 6 7 59. x3 - 9x 0 60. x3 - x 0 In 61 and 62 (a) find the zeros of each function,(b) factor each function over the real numbers, (c) graph each function by hand, and (d) solve f1x2 6 0. 61. f1x2 = 2x4 + 11x3 - 11x2 - 104x - 48 62. f1x2 = 4x5 - 19x4 + 32x3 - 31x2 + 28x - 12 In 6366, (a) graph each function by hand, and (b) solve f1x2 0. 63. f1x2 = x2 + 5x - 6 x2 - 4x + 4 64. f1x2 = 2x2 + 9x + 9 x2 - 4 65. f1x2 = x3 + 2x2 - 11x - 12 x2 - x - 6 66. f1x2 = x3 - 6x2 + 9x - 4 x2 + x - 20 Chapter Review 243 bottom of the fall. The stiffness of the cord is related to the amount of stretch by the equation K = 2W1S + L2 S2 where W = weight of the jumper (pounds) K = cords stiffness (pounds per foot) L = free length of the cord (feet) S = stretch (feet) (a) A 150-pound person plans to jump off a ledge attached to a cord of length 42 feet. If the stiffness of the cord is no less than 16 pounds per foot, how much will the cord stretch? (b) If safety requirements will not permit the jumper to get any closer than 3 feet to the ground, what is the minimum height required for the ledge in part (a)?
Limits and Discontinuity Notes Limits of sequences: 1/2 , k approaches ∞, and the fraction approaches 0. 0 is the limit as k approaches ∞. (2 -1)/2 , k approaches ∞, and the fraction approaches 1. 1 is the limit as k approaches ∞. Limits of average rates of change: finding final instantaneous velocity, calculate the rate of change over the last quarter second. Can’t find actual final velocity because can’t use r= ∆s/∆t when ∆t is 0, we just approach a value as ∆t approaches 0(this is a derivative). In general, limits help us discuss what happens when we let things get infinitely lim f (x)=L small, infinitely large, or close to some number. x→ c , as f(x) approaches L, as x gets clo
