Question

If [.] denotes the greatest integer function then $\underset{x\to 0}{lim}\left[\frac{x^2}{tanx.sinx}\right]=$

• A. 0
• B. 1
• C. -1
• D. does not exist

Answer 1

The correct option is B 1

From the graph of x, sin x and tan x we see that,
$\frac{tanx.sinx}{x^2}<1$
Or,
$\frac{x^2}{tanx.sinx}>1$
Thus, $1<\frac{x^2}{tanx.sinx}<2$
Hence,
$\left[\frac{x^2}{tanx.sinx}\right]=1$
Or,
${lim}_{x\to 0}\left[\frac{x^2}{tanx.sinx}\right]=1$