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 the greatest integral function) is

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

Answer 1

Answer: (B)

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