\(\lim\limits_{x\to 0} \frac{1 - \cos x} x \)
\(= \lim\limits_{x\to 0} \frac{2\sin^2 \frac x2}{x}\)
\(= 2\left[\lim\limits_{x\to 0} \frac{\sin \frac x2}{\frac x2 \times 2}.\lim\limits_{x\to 0} \sin \frac x2\right]\)
\(= 2 \left[\frac 12 \times 0\right]\)
\(= 0\)
