I have a question in a past paper. Is the following continuous at x=0:

f(x)=$\displaystyle (1-cos(x))/x$

The model answer says no it is not continuous at x=0 and you would have to define f(0)=0 to make it continuous.

I understand that a/0 is undefined but in this case the numerator is 0 at the same x point that the denominator is thus we have 0/0. Is that still considered undefined and why?

Thanks