please provide me with the code and the report in details

Part A:

The following three methods are proposed to compute $111/6.$ Using Matlab, determine if they converge and for the convergent methods rank them in order, based on their apparent speed of convergence, assuming p$0=2.$

Method $1$:

Method $2$:

Method $3$:

$.$

pn $=$ pn$1$

p

$6$

n$1$

$.$

$11$

$6$p

$5$

n$1$

$.$

pn $=$ pn$120$

p

$6$

n$1$

$11$

pn $=$ pn$124$

p

$6$

n$1$

$11$

Part B:

Present a table or plots of the absolute error$|$ p $$ p $|$ against$$n to further illustrate the convergence or divergence of the iterations in Part A$.$

Part C:

Using$$your computed errors, estimate the order of convergence$\backslash$alpha and the asymptotic error constant$\backslash$lambda for each convergent iteration. Explain clearly how you compute each constant. As part of your explanation, you may wish to refer to your table or plot$($s$)$ from Part B$,$ or introduce a new table or plot.

There are several possible ways to compute the constants. Some methods are better than others, and will be assigned higher grades.

NOTES:

$$ See$$De$$nition $2\mathrm{.}7$ on page $78$ of the text for the de$$nition of$\backslash$alpha and$\backslash$lambda $.$

$$ Refer to the Guidelines for Computing Assignments for general rules, requirements on written communication, information on the graphical presentation, and the grading scheme.

$$ Remember that you will be marked based on your report so make sure that it includes all of your results. We do not normally access your submitted Matlab scripts, but we may if we have academic integrity or other concerns.