Question

The value of $\underset{x\to 0}{lim}\left[\frac{3\sin 3x}{x}\right]-\left[\frac{2\sin 2x}{x}\right]$ ( where, [.] denotes greatest integer function) is

• A. $5$
• B. $3$
• C. $8$
• D. $6$

Answer 1

The correct option is A $5$

${lim}_{x\to 0}\left[\frac{3\sin 3x}{x}\right]-\left[\frac{2\sin 2x}{x}\right]$

Apply L-Hospital's rule

${lim}_{x\to 0}[3\cos 3x\cdot 3-2\cos 2x\cdot 2]$

$=9\cos 0-4\cos 0$

$=9-4=5$