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Unformatted text preview: , , x n } , an arbitrary partition of [0 , 2] , write L f ( P ) and U f ( P ) , the lower sum and the upper sum of f. b) ( 5 points ) For each i = 1 , 2 , , n consider the three numbers x 2 i , x 2 i1 , and 1 3 ( x 2 i1 + x i1 x i + x 2 i ) . Which one of them is the largest and which one is the smaller? 5 c) ( 10 points ) Denote the following sum by M f ( P ) : ( x 1x ) x 2 + x x 1 + x 2 1 3 +( x 2x 1 ) x 2 1 + x 1 x 2 + x 2 2 3 + +( x nx n1 ) x 2 n1 + x n1 x n + x 2 n 3 . Use b) to deduce which one of the numbers L f ( P ) , U f ( P ) , and M f ( P ) is the largest, and which one is the smaller one. d) ( 5 points ) For each i = 1 , 2 , , n say which one of the two numbers ( x ix i1 ) x 2 i1 + x i1 x i + x 2 i 3 , x 3 ix 3 i1 3 is the smaller. 6 e) ( 5 points ) Use a), c) and d) to evaluate R 5 1 3 f ( x ) dx. 7...
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This note was uploaded on 09/22/2009 for the course MATH 1501 taught by Professor Gangbo during the Spring '09 term at University of Georgia Athens.
 Spring '09
 Gangbo
 Math

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