NEWTON'S METHOD

Question

1. There is some starting integer number, called S, that we want to find the square root of. (i.e. we want to find S−−√ ) So prompt the user to enter an integer value between 20 and 400 for S.  We are assuming that the user will enter an integer and not a String or double value.

2. Capture the user's input in an integer variable, named S

3. Calculate the value of the initial guess x0 to be one-half of S. Note that this value will need to be double.

4.Use the general formula x{n+1} = 0.5(x{n} + S/x{n}) to calculate x1 through x9

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Answer 1

https://en.wikipedia.org/wiki/Newton%27s_method

The program will work as follows,

1. Ask the user for a number, store this in an integer variable S
2. Solve equation x^2 - S = 0 using Newton's method
3. f(x) = x^2 - S and f'(x) = 2x, x_{n+1} = x_n - f(x_n)/f'(x_n)
4. We specifically choose the seed value x0 = S/2 as defined in item 3 in the instructions
5. We iterate through Newton's method 9 times to get x1 through x9