Problem $1.$Use Jupyter notebook for this problem. $($Because it says Jupyter Notebook, I would need the solution answer coded in Python$)$

Please don't just write answer on paper, if you know how to solve it please post the final answers to be running in Jupyter Notebook for Python.

Consider the equation

$tanx=x$

a$.$Find the first $5$ digits of the smallest positive root $($i$.$e$.,$ the smallest root greater

than $0)$ using Bisection method. What was the initial interval used for finding the root and why did you choose it$?$

b$.$Find the first $5$ digits of the same root in part $($a$)$ using Newton's method. What

was the initial value used for finding the root?

c$.$Modify the initial value found in part $($b$)$ until Newton's method no longer con$-$

verges. Discuss why Newton's method fails to converge to the smallest positive root when starting at the modified initial value.

d$.$Create a plot comparing the convergence rate of Bisection method and Newton's

method. Discuss your result.