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Q. $\displaystyle\lim_{x \to 0} \frac {1-\cos\,x}{x^2}$ is equal to

KCETKCET 2015Limits and Derivatives

Solution:

$\displaystyle\lim _{x \rightarrow 0} \frac{1-\cos x}{x^{2}} $
$=\displaystyle\lim _{x \rightarrow 0} \frac{\sin x}{2 x} $ [using L' Hospital's rule]
$=\frac{1}{2}$