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Unformatted text preview: as shown on the sketch. (ii) 1 dx dg Calculations here are the same as above. In this case, however, repeating the process moves P along y=x away from the root and the iterations do not converge on the root, as shown in the sketch. The Rule: always choose an ) ( x g x = form corresponding to 1 < dx dg near the root. x 2 length=x 2 x y y=g(x) P root g(x 1 ) y=x (slope=1) x 1 x y root x 1 y=g(x) y=x length=x 2 x y x 1 y=g(x) x 2 P root g(x 1 ) y=x (slope=1) y y=x root x 1 y=g(x)...
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- Spring '10