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$\lim _{x \rightarrow 0} \frac{2 \sin ^{2} 3 x}{x^{2}}$ is equal to
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Verified Answer
The correct answer is:
18
Consider $\lim _{x \rightarrow 0} \frac{2 \sin ^{2} 3 x}{x^{2}}$
$\begin{array}{l}
=2 \cdot \lim _{x \rightarrow 0}\left[\frac{\sin 3 x}{x}\right]^{2}=2 \cdot \lim _{x \rightarrow 0}\left[3 \frac{\sin 3 x}{3 x}\right]^{2} \\
=2.9 \lim _{x \rightarrow 0}\left(\frac{\sin 3 x}{3 x}\right)^{2}=18 \times 1=18
\end{array}$
$\begin{array}{l}
=2 \cdot \lim _{x \rightarrow 0}\left[\frac{\sin 3 x}{x}\right]^{2}=2 \cdot \lim _{x \rightarrow 0}\left[3 \frac{\sin 3 x}{3 x}\right]^{2} \\
=2.9 \lim _{x \rightarrow 0}\left(\frac{\sin 3 x}{3 x}\right)^{2}=18 \times 1=18
\end{array}$
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