Calculus I

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  1. Formula for Average Velocity
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  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
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    if and only if _________ and __________
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  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)
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  6. Limit Laws

    Suppose that c is a constant and the limits

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    exist, Then:

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

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

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  13. If Image Upload 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
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  14. Squeeze theorem:

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

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

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

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

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    if for every number Image Upload > 0 there is a corresponding number Image Upload > 0 such that:
    |f(x) - L| < Image Upload whenever a < x < a + Image Upload
  18. When a limit = 1/0 it is:
    undefined
  19. When a limit = 0/0 it is
    Indeterminate
Author:
clkottke
ID:
149285
Card Set:
Calculus I
Updated:
2012-04-22 19:47:04
Tags:
calculus
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Description:
Calculus I part 1, limits
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