8.1 Arc Length

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Author:
jojobean0203
ID:
229269
Filename:
8.1 Arc Length
Updated:
2013-08-06 02:15:32
Tags:
calc
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Description:
calc
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  1. How to find the length of a polygon?
    • 1.) treat segment endpoints as coordinates
    • 2.) use distance formula to find length between endpoints
    • 3.) add length of all segments
  2. How is the arc length of a curve defined?
    • 1.) approximate arc length with a polygon
    • 2.) think of a series of polygons with an increasing # of segments
    • 3.) take limit as the # of segments in the polygon increases to infinity
  3. graph of curve C is y = f(x)
    x
    is in the interv [ a , b ]
    how to get C's polygon approximation?
    • 1.) divide interval [ a, b ] by n segments
    • 2.) resulting subintervals:
    • endpoints: x0, x1, ..., xn
    • width:
  4. If :  yi = f(xi)
              =
    f(endpoint)

    Then: the point P(xi , yi) ___________
    & the polygon with vertexes P0, P1,...Pn ______________
    is on C

    • approximates  C
  5. What is the process for defining arc length?
    • 1.) divide curve into many small parts
    • 2.) find & add their approximate lengths
    • 3.) the take limit as n approaches infinity
  6. What makes a function "smooth"?
    • - it has a continuous dx
    • - a small  in x yields a small  in f'(x)

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