2:02 @ X $ 4 0 40% . . . Title Chapter 1: Limits and Continuity EXERCISES BASIC SKILLS PRACTICE For Exercises 1 - 3, use the graph of f to estimate (a) lim f(x) and (b) lim f(x) (i.e., find the end behavior of the function). If a limit does not exist because the function has infinite behavior, use limit notation to describe the infinite behavior. 1. -7 -... ... 2. 3. ........ TAMU 113 113 (125 of 930)For Exercises 4 - 15, find the limit. If the limit does not exist because the function has infinite behavior, use limit notation to describe the infinite behavior. 4. lim -3.x *-+00 5. lim -7x5 X - -00 6. lim (4x2 + 7x-5) 7. lim (-4x7 +2x-9) 8. lim -8.x2 +4 x--00 2.x3 -9x 9. lim- 2x3 - 3 x-+-00 -4x+7 7,9,15 and 17 10. lim - 4x2 + 7 x-+00 5x -8 11. lim - -x -x x-+-00 4.x2 + 1 12. lim 5e-4x *-+00 13. lim 2e3x *-+00 14. lim -3e-x *-4-00 15. lim 4ex - 00 For Exercises 16 - 19, find the x-values of any (a) holes and (b) vertical asymptotes of the function. 16. f(x) = - (x+2)(x-4) (x -4)(2x+5) 17. f (x ) = (x+7)(x-9) (x- 9)(4x -5) 18. f(x) = (2x - 3)(x+6) (2x + 3)(x-6) 19. f(x ) = (3x -8)(x+4) - 9)For Exercises 20 - 27, find any horizontal asymptotes of the function. 20. f(x) = -2x6 +5x 21. f(x) =-503-12-9 22. f (x) = - 2x - 7 4x2 + 3 23. f (x) = 3x3 - 7 4x + 3 24. f(x) = -9x2 + 3x 2x2 - 5 25. f(x) = -21 +4 24,27 and 31 3x2 + 7x 26. f(x) = 4e-3x 27. f(x) = -3e6x INTERMEDIATE SKILLS PRACTICE For Exercises 28 - 37, find the limit. If the limit does not exist because the function has infinite behavior, use limit notation to describe the infinite behavior. 28. lim (2x3 + 18 -4x2) 29. lim (32-3x3 + 10xl') 30. lim 4x3 - 8x10 +4x6 * -+ 00 8.x2 - 7x+5 31. lim 12 +4x + x X-2-00-19x6 -4x2 32. lim - 4x2 -5x+3x3 x-+0 15x - 3x5 - x4 33. lim 4x2+ 7x3 - 9 x-4-00 -x3-7x+8 5 34. lim x-+00 8+ e2x6 35. lim X--00 03x - 12 507x 36. lim X-woo e-2x + 9 37. lim For Exercises 38 - 43, find any (a) holes and (b) vertical asymptotes of the function. For each vertical asymptote, describe the infinite behavior using limit notation. 38. f (x) = (2x+7)? ( x -4) (x+3)(2x+7) 39. f(x) = (x-17)(x+4) (3x-8)(x+4)2 40. f(x) = _ * +3x-28 x2 - x - 12 39,41,44 and47 41. f(x) = = 2x- +5x-3 2x2 - 9x +4 42. f (x ) = 3x + 11x2 -4x 2x3 -3x2 - 2x 43. f ( x ) = _ x -3x2 -28x 14 -4x3+3x2 For Exercises 44 - 51, find any horizontal asymptotes of the function. If there are none, describe the end behavior using limit notation. 44. f (x) = 5x2 -7x4 + 3x 4x- 14 45. f(x) = 10x -4x-x3 3.x2 + 7x5 46. f(x) = =14x 7 -4x-5 3x2 - 8x 47. f (x) = = 25x4 - x9 8xll -4x2 + 19 48. f(x) = 5 1 -2e-2x49. f(x) = - 10 e4x + 5 50. f(x) = - 7+3e3x 4-803x 51. f (x) = = 5-e-4x 3e-4x - 1 For Exercises 52 - 55, find any (a) horizontal asymptotes, (b) holes, and (c) vertical asymptotes of the function. 52. f(x) = 2x2 - x-21 3x2 + 14x-5 4x2 -9 53. f(x) = 2x2 + 5x-12 54. f ( x ) = = 8+x-12x x2+3x-4 53 only 55. f(x) = - x3 -x2 - 6x 14 -5x3- 14x2 MASTERY PRACTICE For Exercises 56 - 66, find the limit. If the limit does not exist because the function has infinite behavior, use limit notation to describe the infinite behavior. 56. lim ((x+2)(-7+2x)) * -+00 9x2 - x6 +3x 57. lim x-+-00 31x7-42x9 + V5x3 -4e2x - 5e-2.x 58. lim - x-+00 10 + e-3x+ 7e2x 59. lim ((-2x+ 3) (5+4x2)) -7x10 + x 25 60. lim - x-+00 -14+3x10 61. lim - 16x7+9x8 - n x-+00 -2x8 - 9x7+3 62. lim (2x2 -3) (10+8.x))6ex + 5e-2x 63. lim 4-00 -25x + ex - 13 -402x - 5e-2x 64. lim x-+-00 10+ e-3x + 7e4x 65. lim (4x3 -5)(-3x3 + 10x)) ex + 7e-8x 66. lim 1-+0o e-3x - 5e2x For Exercises 67 - 73, find any horizontal asymptotes of the function. If there are none, describe the end behavior using limit notation. 67. f(x) = 3ex + 5e-2x -3x + 4e8x 68. f (x) = -41x - 3x2 + 7x8 x+2x8 - 6.x3 4e-*+ 2x 69. f(x) = 1 +6e-*+ 2e-3x 63 and 75 V2x40 - 7120 +5 70. f (x) = - -6x38 +2x9-8 2e-4x - 25x 71. f (x) = = e2x - 6e* + 8 207* -4e-5x 72. f (x) = 100+ 3e-5x + 5e8x 73. f (x) = 7x2 -4x9 + 1 4x5-18+2x10 For Exercises 74 - 76, find any (a) horizontal asymptotes, (b) holes, and (c) vertical asymptotes of the function. If there are no horizontal asymptotes, describe the end behavior using limit notation. For each vertical asymptote, describe the infinite behavior using limit notation. 74. f(x) = 2x + 13x2 -45x x+9 75. f ( x) = 8x-+28x-60 5x2 -8x-21 76. f(x) = 3x3 - 15x2 - 18x 4x4 -4For Exercises 1 - 4, use the graph of f to determine the x-value(s) where f is discontinuous. State the condition in the definition of continuity at a point that fails first at each x-value mathematically. if.(): 3 -.fir)-1 2. ALL.... 3