Nihar is ill, and he goes to the hospital. The hospital treats people who can solve a certain calculus problem, for free. Nihar, being a prodigy took less than 1 minute to solve the problem and got himself treated for free. The problem was as follows:

\[\displaystyle \lim_{x\to 0} \dfrac {1 - \cos (x)}{x^2} = \, ?\]

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