lim _{x rightarrow 0} frac{2 sin x-sin 2 x}{x | vedclass

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(A) Let $L = \lim _{x \rightarrow 0} \frac{2 \sin x - \sin 2x}{x^3}$ (which is of the form $\frac{0}{0}$).Applying $L$-Hospital rule:$L = \lim _{x \ri

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(A) Let $L = \lim _{x \rightarrow 0} \frac{2 \sin x - \sin 2x}{x^3}$ (which is of the form $\frac{0}{0}$).Applying $L$-Hospital rule:$L = \lim _{x \rightarrow 0} \frac{2 \cos x - 2 \cos 2x}{3x^2}$ (which is of the form $\frac{0}{0}$).Applying $L$-Hospital rule again:$L = \lim _{x \rightarrow 0} \frac{-2 \sin x + 4 \sin 2x}{6x}$ (which is of the form $\frac{0}{0}$).Applying $L$-Hospital rule again:$L = \lim _{x \rightarrow 0} \frac{-2 \cos x + 8 \cos 2x}{6}$.Substituting $x = 0$:$L = \frac{-2 \cos(0) + 8 \cos(0)}{6} = \frac{-2(1) + 8(1)}{6} = \frac{6}{6} = 1$.

$\lim _{x \rightarrow 0} \frac{2 \sin x-\sin 2 x}{x^3}$ is equal to

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