Mid$-$Term Exam #$1$

Q$1)$ The square root of any positive number a can be found using this algorithm. Write MATLAB code to implement the algorithm

Initialize $a$

Initialize $x$ to $\frac{a}{2}$

Repeat $5$ times the following:

Replace $x$ by $\frac{x+\frac{a}{x}}{2}$

Display $x$

Compute $y=\sqrt[\phantom{2}]{a}$

Compute the error between $y$ and $x,$ Error $=|y-x|$

Display the Error

Stop

$(30$ point$)$