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## Homework Statement

"Determine the first two non-vanishing terms in the Taylor series of [tex]\frac{1-\cos(x)}{x^2}[/tex] about x = 0 using the definition of the Taylor series (i.e. compute the derivatives of the function)."

So I know how compute the Taylor series about x=0; it involves finding f(0), f'(0), f''(0), etc. But In this particular case, it seems that f(0) and all the derivatives are undefined at x=0. This presents a problem.

I know that I can just replace cos(x) with it's Taylor series, which would make this easy, but the question specifically tells me not to..

What am I missing?