* added type hints and doctests to arithmetic_analysis/newton_method.py
Continuing #2128
Also changed some variable names, made them more descriptive.
* Added type hints and doctests to arithmetic_analysis/newton_method.py
added a type alias for Callable[[float], float] and cleaned up the exception handling
* added type hints and doctests to arithmetic_analysis/newton_method.py
improved exception handling
* Update newton_method.py
Co-authored-by: Christian Clauss <cclauss@me.com>