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Unformatted text preview: dent. Note that the first term on the right hand side of the equation is simply g(x0). Instructing Mathematica to simplify this expression yields: In:= Simplify @ fg1 D Out= c + x0 3-3 x0 2 x1 + 3 x0 x1 2 + x1 H b + a x1 L Subtracting this result from the orginal expression g(x1) yields the error of approximation: In:= g1-fg1 Out=-b x0-a x0 2-x0 3 + b x1 + a x1 2 + x1 3-H b + 2 a x0 + 3 x0 2 L H-x0 + x1 L-1 2 H 2 a + 6 x0 L H-x0 + x1 L 2 In:= Simplify @ % D Out=-H x0-x1 L 3 TaylorSeries.nb 1 Note that if x1-x0<1 then the error term converges to zero faster than x1 approaches x0. TaylorSeries.nb 2...
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This note was uploaded on 11/08/2011 for the course AEB 6533 taught by Professor Moss during the Fall '08 term at University of Florida.
- Fall '08