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Question
\[\lim_{x \to 0} \frac{3 \sin x - \sin 3x}{x^3}\]
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Solution
\[\lim_{x \to 0} \left[ \frac{3 \sin x - \sin \left( 3x \right)}{x^3} \right]\]
\[ = \lim_{x \to 0} \left[ \frac{3 \sin x - \left( 3 \sin x - 4 \sin^3 x \right)}{x^3} \right]\]
\[ = \lim_{x \to 0} \left[ \frac{4 \sin^3 x}{x^3} \right]\]
\[ = \lim_{x \to 0} \left[ 4 \left( \frac{\sin x}{x} \right)^3 \right]\]
\[ = 4 \times 1 = 4\]
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