$2\mathrm{.}1$ Enter: format long. Use mynewton on the function $f(x)=x^5-7,$ with $x_0=2.$ By trial and error, what is the lowest value of $n$ for which the program converges $($stops changing$).$ Compute the error, which is how close the program's answer is to the true value. Compute the residual, which is the program's answer plugged into $f.$ Are the error and residual zero?

$2\mathrm{.}2$ For $f(x)=x^3-4,$ perform $3$ iterations of Newton's method with starting point $x_0=2.($On paper, but use a calculator.$)$ Calculate the solution