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Unformatted text preview: x k ,f ( x k )) to ( x k +1 ,f ( x k +1 )) with straight line segments: note that at one of these points, f ( x ) = x while at the other f ( x ) = x . Show that the line segment joining the points on the curve corresponding to x = x k and x = x k +1 has length at least s k = | f ( x k +1 ) f ( x k ) | = x k +1 + x k = 2 (2 k + 1) + 2 (2 k 1) = 2 p 4 k 4 k 2 1 P ....
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
- Fall '08