Question: Use Theorem 2.3 to show that g(x) = 2x has a unique fixed point on [ 1/3, 1]. Use fixed-point iteration to find an approximation

Use Theorem 2.3 to show that g(x) = 2−x has a unique fixed point on [ 1/3, 1]. Use fixed-point iteration to find an approximation to the fixed point accurate to within 10−4. Use Corollary 2.5 to estimate the number of iterations required to achieve 10−4 accuracy, and compare this theoretical estimate to the number actually needed.

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