Question: 5) Prove, using a theorem covered in class, that g(x) = +0.5 sin(x/2) has a unique fixed point on [0,2]. Use the fixed-point iteration

5) Prove, using a theorem covered in class, that g(x) = +0.5 sin(x/2) has a unique fixed point on [0,2]. Use the fixed-point iteration method to find an approximation to the fixed point that is accurate to within 10-2 (meaning the difference between g(x) and x is within 10-2). Use the theoretical result to estimate the number of iterations required to achieve 10-2 accuracy. How does the theoretical estimate compare to number actually needed?

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