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Unformatted text preview: computer to the next) 4.7 True value: f’ (0.577) = 2,352,911 3digit result with chopping: f’ (0.577) = 216,250, t ε = 90.8% 4digit result with chopping: f’ (0.577) = 2,048,521, t = 12.9% 2 4.12 True value: f (3) = 554 Zero order: f (3) ≈62, t ε = 111.19% First order: f (3) ≈ 78, t = 85.92% Second order: f (3) ≈ 354, t = 36.10% Third order: f (3) ≈ 554, t = 0% 4.14 True value: f (2) = 0.693147. .. Zero order: f (2) = 0, t = 100% First order: f (2) = 1, t = 44.27% Second order: f (2) = 0.5, t = 27.87% Third order: f (2) ≈ 0.833333, t = 20.22% Fourth order: f (2) ≈ 0.583333, t = 15.84% 4.15 True value: f’ (2) = 283 Forward: f’ (2) = 312.8, t E = 29.8 Backward: f’ (2) = 255.2, t E = 27.8 Centrered: f’ (2) = 284, t E = 1 t E based on remainder term in Taylor series: Forward: t E = 28.8 Backward: t E = 28.8 Centrered: t E = 1 4.21...
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 Spring '09
 RAPHAELHAFTKA
 Taylor Series, true value, Chapra

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