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Evaluate x→...

Question

Evaluate $lim x \to 0 \frac{tan 2 x - x}{3 x - sin x}$

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Solution

${lim}_{x \to 0} \frac{tan 2 x - x}{3 x - sin x} = {lim}_{x \to 0} \frac{2 {sec}^{2} 2 x - 1}{3 - cos x} = \frac{2 - 1}{3 - 1} = \frac{1}{2}$

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