# 8.1 Arc Length

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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)
 Author: jojobean0203 ID: 229269 Card Set: 8.1 Arc Length Updated: 2013-08-06 06:15:32 Tags: calc Folders: Description: calc Show Answers: