Question

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

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

Answer 1

Answer: (B)

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