# Write a program that finds roots of a nonlinear equation: 1) Creat...

## Transcribed Text

Write a program that finds roots of a nonlinear equation: 1) Create a Python function, "falsepos(func lb, ub, tolf)", that calculates the root of a function using the false position method given the function name (func), a lower bound (lb), an upper bound (ub), and a tolerance on the value of the equation (tolf) for stopping criteria. The function should return the calculated root and the number of iterations. 2) Create a Python function, "bisect (func, lb, ub, tolf)", that calculates the root of a function using the Bisection method given the function name (func), a lower bound (lb), an upper bound (ub), and a tolerance on the value of the equation (tolf) for stopping criteria. The function should return the calculated root and the number of iterations. Use your Python functions to find the roots of the following equations in the interval of x €[-1,1.5]: a) x tan(x) = 2 b) cos(x) = x c) x3 + sin(x) + cos(x) = 0, Compare the results and the number of iterations for the two methods. Set the stopping criterion for your equation as If(x)l < of where of = 10-3. Challenge: Modify your functions to output the result at each iteration for false position method and Bisection method. Make a graph of the relative errors vs iteration number for the two methods and compare their convergence behavior. For a given value of a and its approximation aapp, the relative error is defined as Er = a dapp a For your calculations consider a as the root found from your function and aapp as the value calculated at each iteration. For example, if you use your functions to find the root of x3 - 8 = 0 in the interval of x € [0, 3] (Ib = 0, ub = 3, tolf = 0.01, x0 = 4), your program should produce a figure similar to Bisection False position 50 40 30 20 10 2 4 6 8 10 iteration number

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