Question

$\underset{x\to 0}{\lim }\frac{3\sin x-4{\sin }^{3}x}{x}$

Answer 1

$\underset{x\to 0}{\lim }\left[\frac{3\sin x-4{\sin }^{3}x}{x}\right]$

= $\underset{x\to 0}{\lim }\left[\frac{\sin 3x}{x}\right]$ $\left[\because {\sin }^{3}A=3\mathrm{sinA}-4{\sin }^3\mathrm{A}\right]$

= $\underset{x\to 0}{\lim }\left[\frac{\sin 3x}{3x}\times 3\right]$

= 1 × 3

= 3