Question

4.10 Team Activity 4 Create a program that will approximate the roots of an equation (i.e. solution to the equation f(x) = 0) using Newton's Method. Newton's Method is an iterative process that approximates the solution using the equation: alt text For this activity, you will approximate the solution for f(x) = x^2. (The derivative of this function is f'(x) = 2x). Your program should accept two user inputs: the number of iterations to perform, i (integer) the starting guess , x0 (float) then output the resulting values of x for each iteration (including the starting guess). For example, if the user wants to perform 3 iterations with a starting guess of x0=1, the result should look like: x 0 = 1.0 x 1 = 0.5 x 2 = 0.25 x 3 = 0.125 Note: The results of this problem have varying numbers of decimal places. Therefore, your print statement should either: (a) use commas to separate strings and variables OR (b) use variable replacement fields with the format() function. If you use replacement fields, we recommend { } in place of {:f} or {:d} which will output the wrong number of decimal places (see zybooks section 2.13 String formatting)

Answer 1

Here is the completed code for this problem. Comments are included, go through it, learn how things work and let me know if you have any doubts or if you need anything to change. If you are satisfied with the solution, please rate the answer. If not, PLEASE let me know before you rate, I’ll help you fix whatever issues. Thanks

Note: Please maintain proper code spacing (indentation), just copy the code part and paste it in your compiler/IDE directly, no modifications required.

#code

#method to calculate the roots using Newton's method
def calculate_roots(num_iterations, starting_guess):
    #initializing x to starting_guess
    x=starting_guess
    #printing starting values
    print('x 0 = {}'.format(x))
    #looping from i=1 to num_iterations
    for i in range(1,num_iterations+1):
        #finding new x (next term) as x^2 divided by 2x
        x=x-(x**2)/(2*x)
        #printing these values after each iteration
        print('x {} = {}'.format(i,x))
    #returning final value of x
    return x


#asking, reading number of iterations and starting guess
i=int(input("Please enter the number of iterations: "))
x0=float(input("Please enter the starting guess: "))
#calculating roots and storing the result
result=calculate_roots(i,x0)
#printing final result, remove if you don't need this.
print('Final result is {}'.format(result))

#output

Please enter the number of iterations: 3
Please enter the starting guess: 1
x 0 = 1.0
x 1 = 0.5
x 2 = 0.25
x 3 = 0.125
Final result is 0.125