Question

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

• A. 197
• B. 198
• C. 199
• D. Does not exist

Answer 1

The correct option is B

198

For x > 0, sin x < x

$\Rightarrow \frac{sinx}{x}<1$

$\therefore \frac{99sinx}{x}<99$

$\Rightarrow \left[\frac{99sinx}{x}\right]$ = 98

and $\frac{x}{sinx}>1$

$\therefore \frac{100x}{sinx}>100$

$\Rightarrow \left[\frac{100x}{sinx}\right]$ = 100

$\therefore \underset{x\to 0}{lim}(\left[\frac{100x}{sinx}\right]+\left[\frac{99sinx}{x}\right])$ = 100+98 = 198