Evaluate \( \lim_{x \to 0} \frac{1 - \cos x}{x^2} \).

Using trigonometric identity \( 1 - \cos x = 2\sin^2(x/2) \), the limit evaluates to \( \lim_{x \to 0} \frac{2\sin^2(x/2)}{x^2} = \frac{1}{2} \).