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 the greatest integral function) is

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

Answer 1

Answer: (B)

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