n 1 g p n g p g p p n p g 00 \u03be n 2 pn p 2 p g00 \u03be n 2 p n p 2 for some \u03be n

N 1 g p n g p g p p n p g 00 ξ n 2 pn p 2 p g00 ξ n

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5 ptsUsing the fact thatf(p) = 0, show that Newton’s method converges quadrat-ically, assumingf0(p) 6 3
4(b)5 ptsUsing Neville’s iterated interpolation, findP0,1,2(0.5) using the followingdata: 5 ptsThe data from the previous problems were given byf(x) =ex-e-x2. Computethe relative and absolute errors from part (a) and part (b). 4

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