In numerical evaluations $0/0$ is undefined $($NaN in MATLAB$/$Octave$).$ In the analysis of signals, it is quite common to see a function expressed as the ratio of two functions such as in these cases, we cannot directly evaluate for $,$ since that would result in $.$ However, the value of this function as approaches $0$ is well$-$defined, and is in fact $1,$ which can be shown using L'Hopital's rule.

This particular ratio of over is a common occurence in signal processing. By the way, it is an even function $($product of odd functions$).$

In signal processing it is convenient to define a related function $.$ Not suprisingly, MATLAB$/$Octave has a built in function called sinc that implements this function. However this requires the Signal Processing Toolbox. For this problem, you will have to write your own version. The key point is dealing eloquently with the case that $.$ To do this you can use logical relation operators. Do not use a for loop or if statements.