# Limit 1-cos x / x^2 as x-->0

Solution:

$\lim_{x\to 0}\frac{1-\cos x}{x^{2}}\\ \\ \Rightarrow \hspace{1cm}\lim_{x\to 0}\frac{2\sin^{2}(\frac{x}{2})}{x^{2}}=\frac{1}{2}\lim_{x\to 0}(\frac{\sin (\frac{x}{2})}{\frac{x}{2}})^{2}=\frac{1}{2}.$

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