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Fixed point iteration, unique solution converge

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Show that for any constants c and d, |d| < 1, the equation x = c + d cos (x) = g(x) has a unique solution alpha. In addition, show that the iteration x_n+1 = c + d cos (x_n) will converge to alpha. Bound the rate of convergence.

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This solution helps with a problem involving fixed point iteration and unique solution coverage.