Question

$\underset{x\to 0}{lim}\frac{3\sin x-\sin 3x}{x.{\tan }^{2}2x}=$

• A. 0
• B. 1
• C. 2
• D. 4

Answer 1

The correct option is B 1

$L{t}_{x\to 0}\frac{3\sin x-\sin 3x}{x.{\tan }^{2}2x}$
$=L{t}_{x\to 0}\frac{3\sin x-(3\sin x-4{\sin }^{3}x)}{x\frac{{\tan }^{2}2x}{(2x{)}^2}(2x{)}^2}$
$=L{t}_{x\to 0}\frac{4{\sin }^{3}x}{4x^3\frac{{\tan }^2\left(2x\right)}{(2x{)}^2}}$
$=1$