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Question
\[\lim_{x \to 0} \frac{3 \sin^2 x - 2 \sin x^2}{3 x^2}\]
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Solution
\[\lim_{x \to 0} \left[ \frac{3 \sin^2 x - 2 \sin x^2}{3 x^2} \right]\]
\[ = \lim_{x \to 0} \left[ \frac{3 \sin^2 x}{3 x^2} - \frac{2 \sin x^2}{3 x^2} \right]\]
\[ = 1 - \frac{2}{3}\]
\[ = \frac{1}{3}\]
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