Given the following function g(x)=sin x+(x-1) we know it has one root in the interval x...

 

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Given the following function g(x)=sin x+(x-1) we know it has one root in the interval x = (0, 1) as shown 1.0 0.5 0.5 1.0 1.5 -0.5 -1.0 The root is r0.319942. Please write a program for each of the following methods to get the root correct within 4 decimal places, i.e., your root (or answer) x, should satisfy |xr| < 0.5 10-4. Also, please indicate how many iteration steps you need and estimate (either by hand or by computer programming) how many floating-point operations needed to achieve your results from the initial (given) conditions: Problems 1.1 Use the bisection method with a given internal a = 0 and b = 1. Problems 1.2 Use Newton's method with the given initial root x0 = 0.8. Problems 1.3 Use the Secant method with two given initial roots x = 0 and roots x = 1. Problems 1.4 Use the fixed-point iterations to find a fixed-point starting from x0 = 1 for g(x). (Hint: fpr 2.0527. You might need to convert the equation so that it converges). Given the following function g(x)=sin x+(x-1) we know it has one root in the interval x = (0, 1) as shown 1.0 0.5 0.5 1.0 1.5 -0.5 -1.0 The root is r0.319942. Please write a program for each of the following methods to get the root correct within 4 decimal places, i.e., your root (or answer) x, should satisfy |xr| < 0.5 10-4. Also, please indicate how many iteration steps you need and estimate (either by hand or by computer programming) how many floating-point operations needed to achieve your results from the initial (given) conditions: Problems 1.1 Use the bisection method with a given internal a = 0 and b = 1. Problems 1.2 Use Newton's method with the given initial root x0 = 0.8. Problems 1.3 Use the Secant method with two given initial roots x = 0 and roots x = 1. Problems 1.4 Use the fixed-point iterations to find a fixed-point starting from x0 = 1 for g(x). (Hint: fpr 2.0527. You might need to convert the equation so that it converges).