Q$1)$ In this question, you asked to write a MATLAB code for the following algorithm. This algorithm

describes an iterative method called the Babylonian method for finding the square root of a given

positive number $S.$

Algorithm $1$ The Babylonian square$-$root algorithm

Require: Initial positive guess $x_0,$ a prespecified tolerance ${}_S,$ maximum number of iterations.

Set $i=0$

$x_{i+1}=\frac{x_i+\frac{S}{x_i}}{2}$

Calculate $|{}_a|=|\frac{x_{i+1}-x_i}{x_{i+1}}|100\%$

if The stopping criterion is satisfied or the maximum number of iterations is reached then

Stop

else

$i=i+1$

Go back to Step $2.$

end if

Output: $x^{**}=x_{i+1}$~~$\sqrt[\phantom{2}]{S}$

DO the following tasks:

a$)$ Write a MATLAB code for the Algorithm $1$ using the FOR$-$END loop command. Use the ta$-$

ble command to print the results. Remember: you need to use the break command to stop the

algorithm when

b$)$ Write a MATLAB code for the Algorithm $1$ using the WHILE$-$END loop command. Use the

table command to print the results.