AP Calculus final

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Sbjohnson
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302889
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AP Calculus final
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2015-05-18 01:04:44
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Calculus
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AP Calculus final flashcards
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  1. critical point
       or undefined
  2.    or undefined
    critical point
  3. inc function f(x)
    f'>0
  4. f'>0
    inc function f(x)
  5. dec function f(x)
    f'<0
  6. f'<0
    dec function f(x)
  7. concavity inc slope
    f''>0
  8. f''>0
    concavity inc slope
  9. concavity dec slope
    f''<0
  10. f''<0
    concavity dec slope
  11. local minimum
      goes (-,0,+) or (-,DNE,+) or 
  12.   goes (-,0,+) or (-,DNE,+) or 
    local minimum
  13. local maximum
      goes (+,0,-) or (+,DNE,-) or
  14.   goes (+,0,-) or (+,DNE,-) or
    local maximum
  15. point of inflection
    • f''=0 or DNE and concavity changes
    •   goes from (+ to -), (- to +)
  16. f''=0 or DNE and concavity changes
      goes (+ to -),(- to +)
    point of inflection
  17. abs. max/min
    eval. crit# & endpoints or discuss "always inc or always dec"
  18. eval. crit# & endpoints or discuss "always inc or always dec"
    abs. max/min
  19. intermediate value theorem
    • if the function f(x) is continuous on [a,b], for all k between f(a) and f(b), there exists at least one number x=c in the open interval:
    • (a,b) such that f(c)=k
  20. if the function f(x) is continuous on [a,b], for all k between f(a) and f(b), there exists at least one number x=c in the open interval:(a,b) such that f(c)=k
    intermediate value theorem
  21. extreme value theorem
    if the function f(x) is continuous on [a,b], then there exists an absolute max and min on that interval
  22. if the function f(x) is continuous on [a,b], then there exists an absolute max and min on that interval
    extreme value theorem
  23. Rolle's theorem
    • if the function f(x) is continuous on [a,b], AND
    • differential on the interval (a,b), AND
    • f(a)=f(b), then there is at least on number
    • x=c in (a,b) such that f'(c)=0
  24. if the function f(x) is continuous on [a,b], ANDdifferential on the interval (a,b), ANDf(a)=f(b), then there is at least on numberx=c in (a,b) such that f'(c)=0
    Rolle's theorem
  25. mean value theorem
    • If the function f(x) is continuous on [a,b], AND
    • differential on the interval (a,b), then
    • there is at least one number x=c in (a,b)
    • such that 

  26. If the function f(x) is continuous on [a,b], AND
    differential on the interval (a,b), then
    there is at least one number x=c in (a,b)
    such that 
    mean value theorem
  27. MVT of Integrals i.e. AVERAGE VALUE
    • If the function f(x) is continuous on [a,b] and differential on the interval (a,b), then there exists at least one number x=c on (a,b) such that





    This value f(c) is the "average value" of the function on the interval [a,b].
  28. If the function f(x) is continuous on [a,b] and differential on the interval (a,b), then there exists at least one number x=c on (a,b) such that






    This value f(c) is the "average value" of the function on the interval [a,b].
    MVT of Integrals i.e. AVERAGE VALUE
  29. Limit Strategies
    • Factor and cancel, rationalize numerator, u-sub HA rules:

  30. Factor and cancel, rationalize numerator, u-sub HA rules:


    Limit Strategies
  31. To find all HA
    Take limit as 
  32. Take limit as 
    To find all HA
  33. Approximation methods for integration
    Rectangles
    Left, right and middle Riemann sums A=bh
  34. Left, right and middle Riemann sums A=bh
    • Approximation methods for integration
    • Rectangles
  35. Approximation methods for integration
    Trapezoids
    • Approximation methods for integration
    • Trapezoids
  36. Effects of inc/dec & concavity on approximation
    Concave up
    M under estimate, T over estimate
  37. Effects of inc/dec & concavity on approximation Concave down
    M over estimate, T under estimate
  38. Effects of inc/dec & concavity on approximation 
    inc
    L=under, R=over
  39. Effects of inc/dec & concavity on approximation 
    dec
    L=over,R=under
  40. First fundamental theory of calculus
    \
  41. First fundamental theory of calculus
  42. Second fundamental theory of calculus
  43. Second fundamental theory of calculus
  44. disk method
  45. disk method
  46. washer method
  47. washer method
  48. volume by cross section (not rotated)






  49. Volume by cross section (not rotated)
  50. Velocity
  51. Velocity
  52. Acceleration
  53. Acceleration
  54. Displacement
  55. Displacement
  56. total distance
  57. total distance
  58. Average velocity
  59. Average velocity

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