Calculus I

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Author:
clkottke
ID:
149285
Filename:
Calculus I
Updated:
2012-04-22 15:47:04
Tags:
calculus
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Description:
Calculus I part 1, limits
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  1. Formula for Average Velocity
  2. The slopes of the _______ line is the ______ of the slopes of the secant lines.
    • tangent
    • limit
  3. The slope of the tangent equals _______________
    instantaneous velocity


  4. if and only if _________ and __________


  5. The line x=a is called a vertical symptote of the curve y = f(x) if at least one of the following is true: (6)




  6. Limit Laws

    Suppose that c is a constant and the limits

    and

    exist, Then:

















    if
    • c
    • The limit of a constant is the constant
  7. =
    where n is a positive integer
    if n is even, we assume that a > 0.


  8. where n is a positive integer
    if n is even, we assume that
  9. If a polynomial or a rational function and a is in the domain of f, then

  10. If for all x in an open interval that conatins a (except possibly at a) and the limits of f and g both exist as x approaches a, then
  11. Squeeze theorem:

    If for all x in an open interval that contains a (except possibly at a) and



    THEN:
  12. Let f be a function on some open interval that contains the number a, except possibly at a itself.



    if for every number > 0 there is a corresponding number > 0 such that:
    |f(x) - L| < whenever 0 < | x - a| <
  13. Definition of Left-Hand Limit



    if for every number > 0 there is a corresponding number > 0 such that:
    |f(x)-L| < whenever < x < a
  14. Definition of Right-Hand limit



    if for every number > 0 there is a corresponding number > 0 such that:
    |f(x) - L| < whenever a < x < a +
  15. When a limit = 1/0 it is:
    undefined
  16. When a limit = 0/0 it is
    Indeterminate

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