Digitopolis - The Land of Numbers

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Author:
mattrcherry
ID:
211333
Filename:
Digitopolis - The Land of Numbers
Updated:
2013-04-11 01:20:16
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Poopenheim
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Description:
This is a Calculous Study Guide for my Cal 1 class.
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  1. Differentiate


  2. Differentiate 


  3. Differentiate

  4. Differentiate

  5. Differentiate

  6. Differentiate

  7. Differentiate

    y=sin(x)
  8. Differentiate

    y=cos(x)
  9. What is the Tangent Line Equation?
  10. Differentiate

  11. Differentiate

  12. ReWrite

  13. Rewrite

  14. Differentiate

    y=f(g(h(x)))
  15. Differentiate

    y=log(x)
  16. Rewrite

  17. Differentiate

    y=sec(x)
  18. Differentiate

    y=log(g(x)
        or     
  19. Rewrite

    log(ab)=?
    log(ab)=log(a)+log(b)
  20. Rewrite

  21. Rewrite

  22. Differentiate

  23. Differentiate

    y=arcsin(x)
  24. Differentiate

    y=arcsec(x)
  25. Rewrite

  26. Differentiate


    y=arctan(x)
  27. Rewrite

  28. ReWrite

  29. Rewrite

  30. Rewrite

  31. Rewrite

  32. Tangent Line Formula:



  33. What is the Normal Line Formula?
  34. Differentiate

    y=tan(x)
  35. Differentiate

    y=csc(x)
  36. Differentiate

    y=cot(x)
  37. Differentiate

    y=sec(x)
  38. Rewrite

    sin(a+b)=?
    sin(a+b)=cos(a)sin(b)+sin(a)cos(b)
  39. Rewrite

    sin(2x)=?
    sin(2x)=sin(x+x)

    =

    sin(x)cos(x)+cos(x)sin(x)
  40. Solve

  41. Solve

  42. Rewrite

    cos(x)sin(x)=?
  43. Rewrite

    sin(x)sec(x)=?
    sin(x)sec(x)=tan(x)
  44. Functions:

    In what "form" will a function become a Vertical Asymptote?
  45. Functions

    In what "form" will a function have a hole?
    When a point is undefined.


     
  46. Functions:

    Describe a Polynomial
    A smooth, well behaved function.

    Ex:

  47. Functions:

    Describe a Rational Function.
    A polynomial multiplied, or divided by, another polynomial.

    Ex:

  48. Functions:

    Describe an exponential function.
    A function whose variable is the exponent of the function. 

  49. Functions:

    Describe a Horizontal Asymptote.
    When a function's limit as it approaches positive or negative infinity is a real number, that is it's Horizontal Asymptote.


     
  50. Rewrite

  51. Functions:

    What are some of the other terms for a prime function?

    The derivative of a function.

    The rate of change(at a given point) of a function.

    The slope of a function.

    The velocity of a function.
  52. Differentiate 

    Rewrite and Differentiate:

    Since conventional methods would have messy results, rewrite your function. 

  53. Trig Functions

    Give 3 different trig variations for this function:

    Sin(x)
    Tan(x)Cos(x)

    1/Csc(x)

    Tan(x)/Sec(x)
  54. l' Hopital's Rule

    In what two function scenarios can you implement the l' Hopital's Rule?
    When the functions are of the forms:

    • 0/0
    • or
    • Infinity/Infinity
  55. Volume

    What is the volume of a cone?
  56. l' Hopital's Rule

    What effect does l' Hopital's Rule have on your function?
  57. l' Hopital's Rule

    What are the 5 indeterminate "forms"?
    • 1- 
    • 2-
    • 3-
    • 4-
    • 5-
  58. Functions

    Extreme values of a function only occur at what points(p)?




    or when P is a boundary point of f's domain.
  59. Multiplicity

    What occurs when a function passes through a critical point where the multiplicity is even?
    It changes signs.

    • From + to - 
    • or
    • From - to +
  60. Area

    What is the Area of a triangle?
  61. Area 

    What is the Area of a circle?
  62. Circumference

    What is the circumference of a circle?
  63. Memory Tools

    Some Old Hags...
    Can't Always Hide

    Their Old Age
  64. Optimization

    What points are of most interest to you when working with Optimization?
    Critical Points and Endpoints.
  65. Volume

    What is the volume of a cylinder?
  66. Volume

    What is the volume of a sphere?
  67. Area

    What is the area of a sphere?
  68. Diameter

    What is the diameter of a circle or sphere?
  69. Formula

    What is the distance formula?
  70. Formula

    What is the Area of a square?
    A=xy
  71. Logarithms 

  72. Functions

  73. Logarithms

    Log(1)=?
    Log(1)=0
  74. Formula

    What is the area of a cylinder?
    • The area of the top and bottom: 
    • Plus the area of the sides:

  75. Formula

    What is the volume of a cube?

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