Evaluate _ x 0 2 x x . - Vidyadip

Question

Evaluate $\lim _{x \rightarrow 0} \frac{\sin 2 x}{x}.$

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Answer

$\begin{array}{l}\lim _{x \rightarrow 0} \frac{\sin 2 x}{x}=\lim _{x \rightarrow 0} \frac{2 \sin x \cos x}{x} \\ =2\left[\lim _{x \rightarrow 0} \frac{\sin x}{x}\right]\left(\lim _{x \rightarrow 0} \cos x\right) \\ =2.1 . \cos 0=2.1 . 1=2\end{array}$

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