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Expansions to Remove Indeterminate Form

Evaluate : x...

Question

Evaluate :
$l i m x \to 0 \frac{1 - cos 2 x}{x}$

A

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Solution

The correct option is D 0
$l i m x \to 0 \frac{1 - cos 2 x}{x} = l i m_{x \to 0} \frac{2 {sin}^{2} x}{x}$

$= 2 l i m x \to 0 (\frac{sin x}{x} \times sin x)$

$= 2 (l i m x \to 0 \frac{sin x}{x}) (l i m x \to 0 sin x)$

$= 2 (1) (0) = 0$

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