Q97 / 150 · MHT CET 2021 (23 Sep Shift 2) · Mathematics
$\lim _{x \rightarrow x}\left[\frac{\sqrt{x}-1}{\log x}\right]=$
- Correct answerA$\frac{1}{2}$
- B$2$
- C$-2$
- D$-\frac{1}{2}$
Solution
$$
\begin{aligned}
& \lim _{x \rightarrow x}\left[\frac{\sqrt{x}-1}{\log x}\right] \\
& =\lim _{x \rightarrow 1} \frac{\frac{1}{2 \sqrt{x}}}{\left(\frac{1}{x}\right)} \\
& =\frac{1}{2}
\end{aligned}
$$
... [L' Hospital rule]
Hence, the correct answer is option: 'A'.