Question

$\underset{x\to 0}{lim}(\left[\frac{100x}{\sin x}\right]+\left[\frac{99sinx}{x}\right])$ (where [.] represents the greatest integral function) is

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

Answer 1

The correct option is A 199

$\text{We know that}\underset{x\to 0}{lim}\frac{\sin x}{x}\to 1^{-}and\underset{x\to 0}{lim}\frac{x}{\sin x}\to 1^{+}$
$\text{So,}\underset{x\to 0}{lim}\left[100\frac{x}{\sin x}\right]+\underset{x\to 0}{lim}\left[99\frac{\sin x}{x}\right]=100+99=199.$