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Digitopolis - The Land of Numbers

  1. Differentiate


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  3. Differentiate 


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  4. Differentiate

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  5. Differentiate

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  6. Differentiate

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  7. Differentiate

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  8. Differentiate

    y=sin(x)
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  9. Differentiate

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

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  12. Differentiate

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  14. ReWrite

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  15. Rewrite

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  16. Differentiate

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

    y=log(x)
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  18. Rewrite

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  19. Differentiate

    y=sec(x)
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  20. Differentiate

    y=log(g(x)
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  21. Rewrite

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

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  23. Rewrite

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  24. Differentiate

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  25. Differentiate

    y=arcsin(x)
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  26. Differentiate

    y=arcsec(x)
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  27. Image Upload 40
  28. Rewrite

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  29. Differentiate


    y=arctan(x)
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  30. Rewrite

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  31. ReWrite

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  32. Rewrite

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  33. Rewrite

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  34. Rewrite

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  35. Tangent Line Formula:

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  36. What is the Normal Line Formula?
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  37. Differentiate

    y=tan(x)
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  38. Differentiate

    y=csc(x)
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  39. Differentiate

    y=cot(x)
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  40. Differentiate

    y=sec(x)
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  41. Rewrite

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

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

    =

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

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  44. Solve

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  45. Rewrite

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

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

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

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


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  49. Functions:

    Describe a Polynomial
    A smooth, well behaved function.

    Ex:

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  50. Functions:

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

    Ex:

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  51. Functions:

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

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  52. 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.


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  53. Rewrite

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  54. Functions:

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

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    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.
  55. Differentiate 

    Rewrite and Differentiate:

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

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  56. Trig Functions

    Give 3 different trig variations for this function:

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

    1/Csc(x)

    Tan(x)/Sec(x)
  57. 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
  58. Volume

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

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

    What are the 5 indeterminate "forms"?
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    • 2-Image Upload 83
    • 3-Image Upload 84
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    • 5-Image Upload 86
  61. Functions

    Extreme values of a function only occur at what points(p)?
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    Image Upload 88

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

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

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

    What is the Area of a triangle?
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  64. Area 

    What is the Area of a circle?
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  65. Circumference

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

    Some Old Hags...
    Can't Always Hide

    Their Old Age
  67. Optimization

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

    What is the volume of a cylinder?
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  69. Volume

    What is the volume of a sphere?
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  70. Area

    What is the area of a sphere?
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  71. Diameter

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

    What is the distance formula?
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  73. Formula

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

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  75. Functions

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  76. Logarithms

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

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

    What is the volume of a cube?
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Author
mattrcherry
ID
211333
Card Set
Digitopolis - The Land of Numbers
Description
This is a Calculous Study Guide for my Cal 1 class.
Updated

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