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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

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

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: x_{0}, x_{1}, ..., x_{n}
 width:

If : y_{i} = f(x_{i})
= f(endpoint)
Then: the point P(x_{i }, y_{i}) ___________
& the polygon with vertexes P_{0}, P_{1},...P_{n} ______________

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

What makes a function "smooth"?
  it has a continuous dx
  a small in x yields a small in f'(x)


