Question

The value of $\underset{x\to 0}{lim}(\left[\frac{50x}{{\tan }^{-1}x}\right]+\left[\frac{50x}{\tan x}\right])$ is
(where $[.]$ denotes greatest integer function )

• A. $101$
• B. $100$
• C. $99$
• D. $98$

Answer 1

The correct option is C $99$

Given : $\underset{x\to 0}{lim}(\left[\frac{50x}{{\tan }^{-1}x}\right]+\left[\frac{50x}{\tan x}\right])$
We know that
$\frac{{\tan }^{-1}x}{x}<1\Rightarrow \frac{50x}{{\tan }^{-1}x}>50$ and
$\frac{\tan x}{x}>1\Rightarrow \frac{50x}{\tan x}<50$
$=50+49$
$=99$