7. (a) Since f'(x) = 2x, Newton's method x_{n+1} = x_{n}
- f(x_{n})/f'(x_{n}) reduces to x_{n+1} = x_{n} -
x_{n}^{2}/2x_{n} = x_{n} - x_{n}/2 =
x_{n}/2.

(c) Starting from x_{0} = 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 x^{2} the basin of attraction of 0 is the interval (-1, 1).

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