ࡱ>  ~ bjbj[[ W99688q^))))\\\ q q q q q q q$sJvn1qu\#U\\\1q))'+qaaa\d)) qa\ qaaCo|p)P7.)]8opq0qova_Hv$pvp<\\a\\\\\1q1q`\\\q\\\\v\\\\\\\\\8 X: Mrs.Volynskaya AP Calculus Name: ___________________ Worksheet L.1-2 Refer to the graph to find each limit, if it exists: a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  d.  EMBED Equation.3  e.  EMBED Equation.3  f.  EMBED Equation.3   1. 2.   a. _____ b. _____ c. _____ a. _____ b. _____ c. _____ d. _____ e. _____ f. _____ d. _____ e. _____ f. _____  3. 4.   a. _____ b. _____ c. _____ a. _____ b. _____ c. _____ d. _____ e. _____ f. _____ d. _____ e. _____ f. _____ 5. 6.   a. _____ b. _____ c. _____ a. _____ b. _____ c. _____ d. _____ e. _____ f. _____ d. _____ e. _____ f. _____ 7. 8. 9.    a.  EMBED Equation.3 = _____ a.  EMBED Equation.3 = _____ a.  EMBED Equation.3 = _____ b.  EMBED Equation.3 = _____ b.  EMBED Equation.3 = _____ b.  EMBED Equation.3 = _____ c. f(2) = _____ c.  EMBED Equation.3 = _____ d. f(1) = _____ 10. True or false? _____ a.  EMBED Equation.3 = -1 _____ b.  EMBED Equation.3 = 1 _____ c.  EMBED Equation.3 = 1 _____ d.  EMBED Equation.3 exists _____ e.  EMBED Equation.3 = 1 _____ f.  EMBED Equation.3  DNE _____ g.  EMBED Equation.3 = 1 _____ h.  EMBED Equation.3 =  EMBED Equation.3  _____ i.  EMBED Equation.3 exists _____ j.  EMBED Equation.3 = 1 _____ k.  EMBED Equation.3 exists at every c on the interval (-1,1) _____ l.  EMBED Equation.3 exists at every c on the interval (1,3) Calculus Name: _____________________________ Worksheet L.1-2 Based on the graph evaluate the following. 1.  EMBED Equation.3 = _____ 11.  EMBED Equation.3 = _____ 2.  EMBED Equation.3 = _____ 12.  EMBED Equation.3 = _____ 3.  EMBED Equation.3 = _____ 13.  EMBED Equation.3 = _____ 4.  EMBED Equation.3 = _____ 14. f(6) = _____ 5.  EMBED Equation.3 = _____ 15.  EMBED Equation.3 = _____ 6.  EMBED Equation.3 = _____ 16. f(3) = _____ 7.  EMBED Equation.3 = _____ 17.  EMBED Equation.3 ( _____ 8. f(1) = _____ 18. f("1) ( _____ 9. f(0) = _____ 19. True or False:  EMBED Equation.3 exists at every c on (1,3) 10. f("2) = _____ 20. True or False:  EMBED Equation.3 exists at every c on ("2,1) Evaluate the following. 21.  EMBED Equation.3  = _____ 22.  EMBED Equation.3  = _____ 23.  EMBED Equation.3  = _____ 24.  EMBED Equation.3  = _____ 25.  EMBED Equation.3  = _____ 26.  EMBED Equation.3  = _____ 27.  EMBED Equation.3  = _____ 28.  EMBED Equation.3  = _____ 29.  EMBED Equation.3  = _____ 30.  EMBED Equation.3  = _____ 31.  EMBED Equation.3  = _____ 32.  EMBED Equation.3  = _____ 33.  EMBED Equation.3  = _____ 34.  EMBED Equation.3  = _____ 35.  EMBED Equation.3  = _____ 36.  EMBED Equation.3  = _____ 37.  EMBED Equation.3  = _____ 38.  EMBED Equation.3  = _____ 39.  EMBED Equation.3  = _____ 40.  EMBED Equation.3  = _____ 41.  EMBED Equation.3  = _____ 42.  EMBED Equation.3  = _____   1 2x, x ( 1 43.  EMBED Equation.3 f(x) = x 3, x ( 1 (a graph may help)  x + 2, x ( "1 44.  EMBED Equation.3 f(x) = x2, x ( 1 (a graph may help) 45. Suppose  EMBED Equation.3 and  EMBED Equation.3 find the  EMBED Equation.3  Calculus Name: _____________________________ Worksheet L.2-1 Find the limits. 1.  EMBED Equation.3  2.  EMBED Equation.3  3.  EMBED Equation.3  4.  EMBED Equation.3  5.  EMBED Equation.3  6.  EMBED Equation.3  7.  EMBED Equation.3  8.  EMBED Equation.3  9.  EMBED Equation.3  10.  EMBED Equation.3  11.  EMBED Equation.3  12.  EMBED Equation.3  13.  EMBED Equation.3  14.  EMBED Equation.3  15.  EMBED Equation.3  16.  EMBED Equation.3  17.  EMBED Equation.3  18.  EMBED Equation.3  19.  EMBED Equation.3  20.  EMBED Equation.3  Calculus Name: _____________________________ Worksheet L.2-2 Evaluate the following. 1.  EMBED Equation.3  = 2.  EMBED Equation.3  = 3.  EMBED Equation.3 = 4.  EMBED Equation.3 = 5.  EMBED Equation.3 = 6.  EMBED Equation.3 = 7.  EMBED Equation.3 = 8.  EMBED Equation.3 = 9.  EMBED Equation.3  = 10.  EMBED Equation.3 = 11.  EMBED Equation.3 = 12.  EMBED Equation.3 = 13.  EMBED Equation.3 = 14. EMBED Equation.3 = 15.  EMBED Equation.3 = 16.  EMBED Equation.3 = 17.  EMBED Equation.3 = 18.  EMBED Equation.3 = 19.  EMBED Equation.3 = 20.  EMBED Equation.3 = 21.  EMBED Equation.3 = 22.  EMBED Equation.3 = 23.  EMBED Equation.3 = 24.  EMBED Equation.3 = 25.  EMBED Equation.3 = 26.  EMBED Equation.3 = 27.  EMBED Equation.3 = 28.  EMBED Equation.3 = 29.  EMBED Equation.3 = 30.  EMBED Equation.3 = 31.  EMBED Equation.3 = 32.  EMBED Equation.3 = 33.  EMBED Equation.3 = 34.  EMBED Equation.3 = 35.  EMBED Equation.3 = 36.  EMBED Equation.3 = 37.  EMBED Equation.3 = 38.  EMBED Equation.3 = 39.  EMBED Equation.3 = 40.  EMBED Equation.3 = 41.  EMBED Equation.3 = 42.  EMBED Equation.3 = 43.  EMBED Equation.3 = 44.  EMBED Equation.3  = 45.  EMBED Equation.3 = Calculus Name: _____________________________ Worksheet L.3 Evaluate the following. 1.  EMBED Equation.3  2.  EMBED Equation.3  3.  EMBED Equation.3  4.  EMBED Equation.3  5.  EMBED Equation.3  6.  EMBED Equation.3  7.  EMBED Equation.3  8.  EMBED Equation.3  9.  EMBED Equation.3  10.  EMBED Equation.3  11.  EMBED Equation.3  12.  EMBED Equation.3  13.  EMBED Equation.3  14.  EMBED Equation.3  15.  EMBED Equation.3  16.  EMBED Equation.3  Calculus Name: _____________________________ Worksheet L.4-1 Refer to the graph to find each of the following: the value(s) of x for which the function is discontinuous why it is discontinuous at that value the type of discontinuity whether it is removable (R) or nonremovable (NR) discontinuity 1) 2) 3)   a) ______________ a) ______________ a) ______________ b) ______________ b) ______________ b) ______________ c) ______________ c) ______________ c) ______________ d) ______________ d) ______________ d) ______________ 4) 5) 6) a) ______________ a) ______________ a) ______________ b) ______________ b) ______________ b) ______________ c) ______________ c) ______________ c) ______________ d) ______________ d) ______________ d) ______________ Given the following graph, state for what values of x the function is discontinuous and state why it is discontinuous at that point. Also state what type of discontinuity it is and whether it is removable or nonremovable. Explain how any removable discontinuities should be defined or redefined to make the function continuous.  Where?Why?TypeRemovable (R) or Nonremovable (NR)If R, what values makes it continuous? Find the value of k that makes the function continuous.  EMBED Equation.3  At what points, if any, is the function f(x) = EMBED Equation.3  discontinuous? Calculus Name: _____________________________ Worksheet L.4-2 Draw a graph with the following conditions.  Function #1 f(0) = 0 (  EMBED Equation.3  f(1) = 2 (  EMBED Equation.3  f(-1) = -2 at f(3) there is a non-removable discontinuity at f(-4) there is a removable discontinuity  Function #2  EMBED Equation.3  (  EMBED Equation.3   EMBED Equation.3  (  EMBED Equation.3  f(0) = 0 at f(-4) there is a removable discontinuity  EMBED Equation.3 exists, but the graph is discontinuous  Function #3  EMBED Equation.3  (  EMBED Equation.3   EMBED Equation.3  (  EMBED Equation.3  f(0) = 0 (  EMBED Equation.3   EMBED Equation.3 exists, but the graph is discontinuous Function #4  EMBED Equation.3  (  EMBED Equation.3   EMBED Equation.3  (  EMBED Equation.3  f(-1) = 0 ( f(2) = 1  EMBED Equation.3  does not exist Function #5 f(-3) = 0 ( f(0) = 3  EMBED Equation.3  (  EMBED Equation.3   EMBED Equation.3  at f(5) there is a removable discontinuity  EMBED Equation.3  does not exist  Function #6  EMBED Equation.3  (  EMBED Equation.3   EMBED Equation.3  (  EMBED Equation.3  f(0) = 1  EMBED Equation.3 exists, but the graph is discontinuous  Function #7 f(0) = 0 (  EMBED Equation.3  f(2) = 1 (  EMBED Equation.3  f(-2) = -4  EMBED Equation.3  does not exist  EMBED Equation.3 exists, but the graph is discontinuous Function #8  EMBED Equation.3  (  EMBED Equation.3   EMBED Equation.3  (  EMBED Equation.3   EMBED Equation.3  (  EMBED Equation.3  f(0) = 2 at f(-5) there is a non-removable discontinuity Calculus Name: _____________________________ Limits Practice Test       Refer to the graph to evaluate the following: 1. _______  EMBED Equation.3  2. _______  EMBED Equation.3  3. _______  EMBED Equation.3  4. _______  EMBED Equation.3  5. _______  EMBED Equation.3  6. _______  EMBED Equation.3  7. _______  EMBED Equation.3  8. _______  EMBED Equation.3  9. _______  EMBED Equation.3  10. _______  EMBED Equation.3  11. _______  EMBED Equation.3  12. _______  EMBED Equation.3  13. _______  EMBED Equation.3  14. _______  EMBED Equation.3  15. _______  EMBED Equation.3  16. _______  EMBED Equation.3  17. _______  EMBED Equation.3  18. _______  EMBED Equation.3  19. _______ True or False:  EMBED Equation.3  exists for every c in the interval (2,10) 20. _______ True or False:  EMBED Equation.3  exists for every c in the interval ("2,2) Refer to the graph to find the following: the value(s) of x for which the function is discontinuous why it is discontinuous at that value the type of discontinuity whether it is a removable (R) or nonremovable (NR) discontinuity if it is removable, how could you make the function continuous at that point? Where?Why?Type?Removable (R) or Nonremovable (NR)?If R, what values make it continuous?21.22.23.24. Evaluate the following. 25. _______  EMBED Equation.3  26. _______  EMBED Equation.3  27. _______  EMBED Equation.3  28. _______  EMBED Equation.3  29. _______  EMBED Equation.3  30. _______  EMBED Equation.3  31. _______  EMBED Equation.3  32. _______  EMBED Equation.3  33. _______  EMBED Equation.3  34. _______  EMBED Equation.3  35. _______  EMBED Equation.3  36. _______  EMBED Equation.3  37. _______  EMBED Equation.3  38. _______  EMBED Equation.3  39. _______  EMBED Equation.3  40. _______  EMBED Equation.3  41. _______  EMBED Equation.3  42. _______  EMBED Equation.3  43. _______  EMBED Equation.3  44. _______  EMBED Equation.3   45. _______  EMBED Equation.3  46. _______  EMBED Equation.3  47. _______  EMBED Equation.3  48. _______  EMBED Equation.3  49. _______  EMBED Equation.3  50. _______  EMBED Equation.3  51. _______  EMBED Equation.3  52. _______  EMBED Equation.3  53. _______  EMBED Equation.3  54. _______  EMBED Equation.3  55. _______  EMBED Equation.3  56. _______  EMBED Equation.3  57. _______  EMBED Equation.3  58. _______  EMBED Equation.3  59. _______  EMBED Equation.3  60. _______  EMBED Equation.3  61. _______  EMBED Equation.3  62. _______  EMBED Equation.3  63. _______  EMBED Equation.3  64. _______  EMBED Equation.3  Find the points of discontinuity. 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