Question

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

• A. $4$
• B. $-4$
• C. $8$
• D. $-8$

Answer 1

The correct option is A $4$

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

$=\underset{x\to 0}{lim}\frac{4{\sin }^{3}x}{x^3}=4\underset{x\to 0}{lim}{\left(\frac{\sin x}{x}\right)}^3=4(1{)}^3=4$