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I need some assistance with this limit when x->0:

[tex]\frac{1-cos(x)}{x^{2}}[/tex]

I do not wish to use L'Hôpital's rule.

What I tried was to write x^2 as x*x, and to separate it so I can use the known limit of cos(x)/x, however it only brought me to the 0*infinity problem.