dx & lim

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  1. Image Upload
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    • m tangent = Image Upload
  2. find equation of secant line
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  3. acceleration
    speed
    velocity
    • speed
    • - absolute value of velocity; does not have direction; magnitude component of velocity
    • - rate of change of position
    • - distance moved per unit of time
    • - s(t) = position fxn
    • velocity
    • - contains both magnitude + direction
    • - s'(t) = velocity fxn
    • acceleration
    • - rate of change of velocity
    • - s"(t) = acceleration nfxn
  4. define derivative of a function
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  5. how is continuity of a function related to limit?
    • f(x) is continuous at x = a when:
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  6. squeeze theorem:

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    range of sin: [-1,1] Image Upload

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    lim as x goes to 0: 0 < 0 < 0
  7. squeeze theorem:

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  8. derive formulas for:
    circle
    - circumference
    - area
    sector
    - length
    - area 
    sphere
    - volume
    - area
    • circle
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    • sector
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    • sphere
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  9. intermed value therem
    • function continuous over closed interval [a, b]
    • if Image Upload:
    • for any value d between f(a) & f(b), excluding f(a) & f(b), there is a c between (a,b) such that f(c) = d
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    Image Upload = 0
    • r is a positive rational number
    • if r > 0 & x > 0, x^r will go to infinity, & 1/x^r will approach 0
  11. principal values of inverse trig fxns
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  12. prove:

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    Image Upload   substitute

    Image Upload  factor out c

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    = c f'(x)
  13. prove
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  14. difference between essential, non-essential, & removal discontinuity
    essential: can't be patched; graph has a break:(2,3) & (2, 5) breaks at x = 2

    • non-essential: removable discontinuity, can be patched,
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    • if these are = (both 9), can patch by defining f(3) = 9
  15. what must be true to repair a discontinuity?
    • the 2 one-sided limits must be the same: the limit of f(x) as x approaches c from the left and right must be equal
    • then f(x) can be repaired by defining f(c) = L
  16. methods for finding/evaluating limit of a fxn
    • using table of values as x gets closer & closer to a
    • graphically
    • algebraically using limit laws
    • using trig identities
  17. if f(x) <g(x) in a neighborhood around x = a; what must be true about their limits?
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  18. Image Upload
    does not exist
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    1
  20. Image Upload
    0
  21. what conditions must be met before taking the limit of a composite function?
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    • for 1 > 2:
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    • f & g are continuous
  22. interval continuity
    • f(x) is continuous on an interval if it is continuous at q # in the interval
    • if f is defined on only one side of an endpoint, continuous at the endpoint means continuous from the right or continuous from the left
  23. the line y = L is a horizontal asymptote of the curve y = f(x) if:
    • either:
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  24. Image Upload
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Author:
jojobean0203
ID:
203202
Card Set:
dx & lim
Updated:
2013-05-27 23:28:57
Tags:
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dx
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