Exercise $4.$ How many iterations do you need until the solution seems to converge? What did it converge to$?$ Tell MATLAB to show

the full accuracy and find the $16-$digit number that the iteration converges to$.$

While using the command history is faster than typing in the same command many times, there is an even better way: tell MATLAB to

do it many times with either a for loop or a while loop.

Both types of loops tell MATLAB to perform a set of commands over and over again. The idea of a for loop is that you are telling

MATLAB to perform a set of command for every element of a list that you supply. For example:

will iterate over the values $3$ to $10$ and perform each of the expressions between the for and the end. At each iteration, the variable, $k$

in this case $($but can be whatever$)$ will be assigned the appropriate value.

Note $1.$ When you type code into MATLAB you might make a mistake and want to start over. Press$\_$CtrlC$\_$to tell MATLAB to erase the

current line and start a new one. Once you start writing a for loop you will not get the command prompt $(x)$ when you press$\_$Enter.

This is$\_$MATLAB's way of telling you that you are in the middle of writing a command. Once you type end $\_$and hit$\_$Enter, MATLAB

$\_$will execute the loop and you'll

get the prompt back. If you started a loop and want to stop in the middle and start over, press$\_$Ctric to get the prompt.