This question has multiple parts.

a$)$ Provide the definition of Order of Convergence given in class. Be sure to describe what each part means $(1$ point$)$

b$)$ Show the order and rate of convergence for Newton Raphson's method $($assuming it converges$).$ You do not need to redo the proof, supplying the end equation will suffice here. $(1$ point$)$

c$)$ A colleague comes to you with help for their NR implementation they did in Fortran. Knowing a$)$ and b$)$ they are troubled by their output $($below$)$ and ask you for advice. Is the output enough information for you to help your colleague $?$ If no$,$ what more information do you need $?$ If yes, explain whether the NR implementation is correct. Give as much detail as possible. $(4$ points$)$