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Unformatted text preview: The overestimate of the area is given by f ( c 1 ) Â· Î” x + f ( c 2 ) Â· Î” x + f ( c 3 ) Â· Î” x = (4 + 5 + 5) Â· 1 = 14 . (b) Underestimate: For the underestimate of the area, we need to take c k to be the value of x for which f ( x ) is the smallest in the k th subinterval. That is, since f is increasing on the negative xaxis, we will take left endpoints for intervals on the negative xaxis; since f is decreasing on the positive xaxis, we will take the right endpoints for intervals on the positive xaxis. So c 1 =2 , c 2 =1 , and c 3 = 1 .21 1 21 1 2 3 4 5 The heights of the rectangles are given in the following table: k c k f ( c k ) 12 f (2) = 5(2) 2 = 1 21 f (1) = 5(1) 2 = 4 3 1 f (1) = 51 2 = 4 The underestimate of the area is given by f ( c 1 ) Â· Î” x + f ( c 2 ) Â· Î” x + f ( c 3 ) Â· Î” x = (1 + 4 + 4) Â· 1 = 9 . 2...
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This note was uploaded on 04/02/2012 for the course MTH 132 taught by Professor Kihyunhyun during the Fall '10 term at Michigan State University.
 Fall '10
 KIHYUNHYUN
 Calculus, Angles

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