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lt.x--->0

3sinx -sin3x /x³

$\lim_{x \to 0} \frac{3 \sin x - \sin 3 x}{x^{3}} = \lim_{x \to 0} \frac{3 \sin x - (3 \sin x - 4 \sin^{3} x)}{x^{3}} [∵ \sin 3 x = 3 \sin x - 4 \sin^{3} x] = \lim_{x \to 0} \frac{3 \sin x - 3 \sin x + 4 \sin^{3} x}{x^{3}} = \lim_{x \to 0} \frac{4 \sin^{3} x}{x^{3}} = \lim_{x \to 0} 4 {(\frac{\sin x}{x})}^{3} = 4 \lim_{x \to 0} {(\frac{\sin x}{x})}^{3} = 4 {(1)}^{3} = 4$

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