Use an appropriate Taylor series to write a MATLAB function M$-$file that approximates

$f(x)=sin(2x)$ for all $x$ with a maximum error of $0\mathrm{.}01.$ That is$,$ your M$-$file should take

values of $x$ as input, return values of $sin(2x)$ as output, but should not use MATLAB's

built$-$in sine function i$.$e$.,sin.m.$

Hint. You might find MATLAB's built$-$in function mod useful in dealing with the

periodicity.