$2\mathrm{.}3$ Modify mybisect and mysecant to solve until the error is bounded by a given tolerance. Use a while loop to do this. How should error be measured? Run your program on the function $f(x)=-e^{-x}+20$ with starting interval $-5,0$ and a tolerance of ${10}^{-10}.$ How many steps does the program use to achieve this tolerance? $($You can count the step by adding $1$ to a counting variable i in the loop of the program.$)$ How big is the final residual $f(x)?$ Turn in your program and a brief summary of the results.

$2\mathrm{.}4$ Perform $3$ iterations of the Regula Falsi method on the function $f(x)=-e^{-x}+20,$ with starting interval $-5,0.($On paper, but use a calculator.$).$ Compare the results with the ones in your Regula Falsi script and make sure your code works well. Show both results here.

$2\mathrm{.}5$ Write a function program myregfalsi that runs the Regula Falsi method until the absolute value of the residual is below a given tolerance. Run your program on the function $f(x)=-e^{-x}+20$ with starting interval $-5,0$ and a tolerance of ${10}^{-10}.$ How many steps does the program use to achieve this tolerance? Turn in your program and a brief summary of the results.

$2\mathrm{.}6$ Compare $4$ methods in terms of how fast they converge to real root.