Question

$\underset{x\to \frac{1}{2}}{lim}\frac{\sin 3\left[x\right]}{\left[x\right]}$, where $\left[x\right]$ denotes the greatest integer $\le x$, is equal to ?

• A. $\frac{3}{2}$
• B. $3$
• C. $1$
• D. none of these

Answer 1

Answer: (B)

$3$

$x\to \frac{1}{2}$

$\left[x\right]\to 0$

${lim}_{x\to \frac{1}{2}}\frac{\sin 3\left[x\right]}{\left[x\right]}\times \frac{3}{3}={lim}_{\left[z\right]\to 0}\frac{3}{1}\times \frac{\sin 3\left[x\right]}{3\left[x\right]}$

$=3\times 1=3$