Math $205-$ Numerical Methods for CE Problems

Newton's Method Assignment

Instructions: Use the mynewton function$\{$:$[>>$f$=$x$^5-7],[>>$f$1=5$x$^4],[>>$x$\_(0)=2],[>>$n$=10],[>$ x$="$ mynewton$($f$,"$f$1","2","10)]$:$\}$

Exercises

$3\mathrm{.}1$ 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?