PP 9.1 - Arc Length We know how to find the distance...

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Unformatted text preview: Arc Length We know how to find the distance between two points. That is equivalent to finding the length of the green line segment in the graph. We want to find the distance between the two points on the blue curve. We want to find the arc length of the blue curve between the two red points, Getting the Formula ion. considerat under arc the of n descriptio the be , ), ( Let b x a x f y = ]. , [ of partition a be ... Let 2 1 b a b x x x x a n = < < < < = n i x f x i i = )), ( , ( P Let i Increasing the number of points of the partition allows us to approximate the arc length using the distance formula. n = 3 n = 5 Then, ) , ( lim length Arc 1 1 =- = = n i i i n P P d L ( 29 =-- - +- = n i i i i i n x f x f x x 1 2 1 2 1 ) ( ) ( ) ( lim = + = n i i i n y x 1 2 2 ) ( ) ( lim ( 29 [ ] = + = n i i i i n x x f x 1 2 * 2 ) ( lim By the Mean Value Theorem applied for each subinterval. ( 29 [ ] =...
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This note was uploaded on 01/21/2011 for the course PHYS 4A 60865 taught by Professor L. oldewurtel during the Fall '09 term at Irvine Valley College.

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PP 9.1 - Arc Length We know how to find the distance...

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