After tinkering with NR method we find another root finding iteration defined by

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This method is implemented in not$\_$newtonraphson.pyDownload not$\_$newtonraphson.py

Modify not$\_$newtonraphson.py Download not$\_$newtonraphson.py so that you can analyze the method by examining output from your own f$($x$)$ examples $($use at least $3$ different f$($x$)\text{'}$s$).$ You do not need to analytically prove your analyses. Please provide your output and explanations as proof.

Describe things such as$,$ but not limited to:

Does this method converge, and if so$,$ what is required for convergence $?$

What conditions would make this method diverge $?$

What is the order of convergence $?$

Is this useful $?$