thomasET_226348_ism12

thomasET_226348_ism12 - 84 24(a Chapter 2 Limits and...

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84 Chapter 2 Limits and Continuity 24. (a) lim 7 (b) lim 7 t t Ä ! Ä ! " " t t œ _ œ _ 25. (a) lim (b) lim x x Ä ! Ä ! " " x (x 1) x (x 1) 2 2 œ _ œ _ (c) lim (d) lim x x Ä " Ä " " " x (x 1) x (x 1) 2 2 œ _ œ _ 26. (a) lim (b) lim x x Ä ! Ä ! " " x (x 1) x (x 1) 1 1 œ _ œ _ (c) lim (d) lim x x Ä " Ä " " " x (x 1) x (x 1) 1 1 œ _ œ _ 27. y 28. y œ œ " " x 1 x 1 29. y 30. y œ œ " # x 4 x 3 3 31. y 1 32. y œ œ œ œ # x 3 2x 2 x 2 x x 1 x 1 " #
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Section 2.5 Infinite Limits and Vertical Asymptotes 85 33. y x 1 34. y x œ œ œ œ " x x x x x 1 x 1 " " " " # 35. y x 36. y x œ œ " œ œ " x x x x x x % $ " " $ " " # % # # % 2 37. y x 38. y x œ œ œ œ x 1 x 1 x x x x " " 39. Here is one possibility. 40. Here is one possibility.
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86 Chapter 2 Limits and Continuity 41. Here is one possibility. 42. Here is one possibility. 43. Here is one possibility. 44. Here is one possibility. 45. Here is one possibility. 46. Here is one possibility. 47. For every real number B 0, we must find a 0 such that for all x, 0 x 0 B. Now, Ê $ $ k k " x B B 0 x x . Choose , then 0 x x ! Í Í Í œ Ê " " " " " " # x x B B B B k k k k k k È È È $ $ B so that
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