Question

$\underset{x\to 0}{lim}\frac{1-\cos x}{x^2}\left[\frac{1}{2}\right]$

Answer 1

$\underset{x\to 0}{lim}\frac{1-\cos x}{x^2}\left(\frac{0}{0}form\right)$

$=u\sin gL-hospitalrule$

$=\underset{x\to 0}{lim}\frac{\sin x}{2x}$

$=\underset{x\to 0}{lim}\frac{1}{2}\left(\frac{\sin x}{x}\right)$

$=\frac{1}{2}\times 1$

$=\frac{1}{2}$