7. (a) Since f'(x) = 2x, Newton's method xn+1 = xn - f(xn)/f'(xn) reduces to xn+1 = xn - xn2/2xn = xn - xn/2 = xn/2.
(c) Starting from x0 = 4, Newton's method converges to 0.
(d) Starting from any of these points, Newton's method converges to 0. The basin of attraction of 0 seems to be all real numbers.
(e) Iterating x2 the basin of attraction of 0 is the interval (-1, 1).
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