function $[$lastTerm$,$ numTerms$]=$ sqrt$2$approx$($errorTol$)$

$\%[$lastTerm$,$ numTerms$]=$ sqrt$2$approx$($ErrorTol$)$

$\%$

$\%$ This function calculates terms of the sequence

$\%$

$\%$ x$(1)=1,$ x$($k$)=($x$($k$-1)+2/$x$($k$-1))/2$

$\%$

$\%$ until the relative error between the Nth term and sqrt$(2)$ falls below

$\%$ a given tolerance.

$\%$

$\%$ Input:

$\%$ errorTol $-$ The tolerance used as the convergence criterion

$\%$ Output:

$\%$ lastTerm $-$ The last term in the sequence $($that meets the tolerance$)$

$\%$ numTerms $-$ The number of terms required to meet the tolerance

ea $=100$;

numTerms $=$ uint$8(1)$;

lastTerm $=$ ;

while ea $>$

lastTerm $=(+2/$lastTerm$)/2$;

ea $=$ abs$(($sqrt$(2)-)/$sqrt$(2))$;

numTerms$=$numTerms$+$ ;

end