Create a PYTHON 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: 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, n (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 fo
Create a PYTHON 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:
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, n (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).
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