Restructure Newton$$s method $($Case Study $3-2)$ by decomposing it into three cooperating functions $($including the original newton method.$).$ The task of testing for the limit is assigned to a function named limitReached$,$ whereas the task of computing a new approximation is assigned to a function named improveEstimate. Each function, in the file named newton.py$,$ expects the relevant arguments and returns an appropriate value. $($LO: $6\mathrm{.}2)$

Instructions

COPY NEWTON.PY

Task $1$: Define the limitReached function.

Task $2$: Define the improveEstimate function.

Task $3$: The newton.py method returns an estimate.

An example of the program is shown below:

Enter a positive number or enter$/$return to quit: $2$

The program's estimate is $1\mathrm{.}4142135623746899$

Python's estimate is $1\mathrm{.}4142135623730951$

Enter a positive number or enter$/$return to quit: $4$

The program's estimate is $2\mathrm{.}0000000929222947$

Python's estimate is $2\mathrm{.}0$

Enter a positive number or enter$/$return to quit: $9$

The program's estimate is $3\mathrm{.}000000001396984$

Python's estimate is $3\mathrm{.}0$

Enter a positive number or enter$/$return to quit: