Question

The value of $\underset{x\to 0}{lim}\frac{x}{5}\left[\frac{x}{2}\right]$ (where $[.]$ denotes the greatest integer function) is

• A. $\frac{2}{5}$
• B. $-\frac{2}{5}$
• C. $0$
• D. $\infty$

Answer 1

The correct option is C $0$

Given,

${lim}_{x\to 0}\left(\frac{x}{5}\left[\frac{x}{2}\right]\right)$

${lim}_{x\to 0}(\frac{x}{5}\cdot \frac{x}{2})$

put the value $x=0$

$=\frac{0}{5}\cdot \frac{0}{2}$

$=0$