Question

The value of $ \displaystyle\lim _{x \rightarrow 0}\left(\left[\frac{100 x}{\sin x}\right]+\left[\frac{99 \sin x}{x}\right]\right)$, where [.] represents greatest integer function, is

• A. 199
• B. 198
• C. 0
• D. None of these

Answer 1

Answer: (B)

We know that $ \displaystyle\lim _{x \rightarrow 0} \frac{\sin x}{x} \rightarrow 1^{-}$
$ \displaystyle\lim _{x \rightarrow 0} \frac{x}{\sin x} \rightarrow 1^{+}$
$\therefore \displaystyle\lim _{x \rightarrow 0}\left[100 \frac{x}{\sin x}\right]+ \displaystyle\lim _{x \rightarrow 0}\left[99 \frac{\sin x}{x}\right]$
$=100+98=198 .$