Question

The value of $\underset{x\to 0}{lim}\left[\frac{x^2}{\sin x\tan x}\right]$, where $[.]$ denotes greatest integer function is:

• A. $0$
• B. $1$
• C. Limit does not exist
• D. None of these

Answer 1

Answer: (B)

$1$

$\underset{x\to 0}{lim}\left[\frac{x^2}{\sin x\tan x}\right]=\underset{x\to 0}{lim}\left[\frac{x^2}{\frac{\sin x}{x}\frac{\tan x}{x}{x}^2}\right]$

$=\underset{x\to 0}{lim}\left[\frac{1}{\frac{\sin x}{x}\frac{\tan x}{x}}\right]=\left[\frac{1}{1\times 1}\right]=\left[1\right]$

$=\left[1\right]$