PRETEND you are trying to computationally solve for the root of the Optimal Thrust equation f$($T$)=$

$0$ using the secant method starting with the initial $$bracket$$ T$1=0\mathrm{.}5,$ T$2=40.$

$($a$)$ Calculate the values of tolX and tolf you would use for the two convergence criteria,

$|$xk $$ xk$-1|<$ tolX

and $|$f$($xk

$)|<$ tolf

$,$ if you were to write your own secant method in MATLAB.

Now $($pretend$)$ you$$ve completed $13$ iterations for T$,$ and the last two iterations have values T$12=$

$16\mathrm{.}410$ and T$13=16\mathrm{.}407.$ For the $$exact solution$$ use the value you got for T in problem $3\mathrm{.}3$ above

to answer the following $($and SHOW YOUR WORK!!$)$:

$($b$)$ What is the $($just plain old$)$ error in the last iteration, T$13?$

$($c$)$ What is the $$proxy$$ for the error for the last iteration?

$($d$)$ What is the $$residual$$ error for the last iteration?

$($e$)$ Based on all your values above, explain whether the process has $$converged$$ yet or not.