2. Solve f(x) = x - 4 sin(x) = 0 and use x = 3 as...

   

Transcribed Image Text:

2. Solve f(x) = x - 4 sin(x) = 0 and use x = 3 as initial guess. a) Do three iterations by hand and tabulate your answer b) Solve using python code and stop the iteration when tol 10-3. c) Plot the original function and your result using matplotlib module. 3. Do three steps (by hand) of secant methods for f(x) = x- 2, x0 = 0 and x = 1. Repeat again by using x0 = 1 and x = 0. Tabulate both result and comment your answer. Redo this by using python code. 4. Implement the bisection, Newton-Raphson and secant method for the following function. You are required to choose your own initial values and range and test which values will give the same solution. Stop your iteration at 10-6. Use python code for this exercise. a) x-2x-5=0 b) ex = x c) x sin(x) = 1 2. Solve f(x) = x - 4 sin(x) = 0 and use x = 3 as initial guess. a) Do three iterations by hand and tabulate your answer b) Solve using python code and stop the iteration when tol 10-3. c) Plot the original function and your result using matplotlib module. 3. Do three steps (by hand) of secant methods for f(x) = x- 2, x0 = 0 and x = 1. Repeat again by using x0 = 1 and x = 0. Tabulate both result and comment your answer. Redo this by using python code. 4. Implement the bisection, Newton-Raphson and secant method for the following function. You are required to choose your own initial values and range and test which values will give the same solution. Stop your iteration at 10-6. Use python code for this exercise. a) x-2x-5=0 b) ex = x c) x sin(x) = 1