Area Example CBD

# Area Example CBD - AREA EXAMPLE: MIDPOINT SUMS FOR f(x) =...

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n 20 0.15 4.502813 i 0 1.00 1 1.15 1.075 1.572188 0.235828 2 1.30 1.225 1.699688 0.254953 3 1.45 1.375 1.804688 0.270703 4 1.60 1.525 1.887188 0.283078 5 1.75 1.675 1.947188 0.292078 6 1.90 1.825 1.984688 0.297703 7 2.05 1.975 1.999688 0.299953 8 2.20 2.125 1.992188 0.298828 9 2.35 2.275 1.962188 0.294328 10 2.50 2.425 1.909688 0.286453 11 2.65 2.575 1.834688 0.275203 12 2.80 2.725 1.737188 0.260578 13 2.95 2.875 1.617188 0.242578 14 3.10 3.025 1.474688 0.221203 15 3.25 3.175 1.309688 0.196453 16 3.40 3.325 1.122188 0.168328 17 3.55 3.475 0.912188 0.136828 18 3.70 3.625 0.679688 0.101953 19 3.85 3.775 0.424688 0.063703 20 4.00 3.925 0.147188 0.022078 x S 20 x i m i f ( m i ) i th area This sheet computes midpoint sum for f ( x ) = 2 x - x 2/2, over [1, 4] with 20 subdivisions. Calculus for Busines Release 2.1, 2 Published and Distr The Mathematical Associa © 2010 by The Arizona Bo The University of Arizo reserved. AREA EXAMPLE: MIDPOINT SUMS FOR f ( x ) = 2x - x2/2

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ess Decisions 2010 tributed by iation of America oard of Regents for ona. All rights .
n 6 0.5 4.531250 i 0 1.000000 1 1.500000 1.250000 1.718750 0.859375 2 2.000000 1.750000 1.968750 0.984375 3 2.500000 2.250000 1.968750 0.984375 4 3.000000 2.750000 1.718750 0.859375 5 3.500000 3.250000 1.218750 0.609375 6 4.000000 3.750000 0.468750 0.234375 7 8 9 10 11 12 13 14 15 16 17 18 19 Number of subintervals ( n) : x S n x i m i f ( m i ) i th area This sheet computes midpoint sum for f ( x ) = 2D x - x 2/2, over [1, 4] with n subdivisions. 1. Set Excel for Automatic Calculation . This is found under Tools / Options / Calculation . 2. Move the Number of subintervals slider to set a value for n in Cell C17 . Clicking on an arrow at the end of a scroll bar increases or decreases n by 1. Cl in the scroll bar increases or decreased n by 10. The width, x , of each subinterval and the sum, Sn , of the areas of all n rectang displayed. This sum is an approximation for the area of the region, R , over [1, 4] that bounded by the x -axis and the graph of f . MIDPOINT SUMS FOR f ( x ) = 2x - x2/2

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20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101

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102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142
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## This note was uploaded on 10/27/2010 for the course ECE 220 taught by Professor Strickland during the Spring '08 term at University of Arizona- Tucson.

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Area Example CBD - AREA EXAMPLE: MIDPOINT SUMS FOR f(x) =...

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