$\lim _{x \rightarrow x}\left[\frac{\sqrt{x}-1}{\log x}\right]=$
$\lim _{x \rightarrow x}\left[\frac{\sqrt{x}-1}{\log x}\right]=$
- $\frac{1}{2}$
- $2$
- $-2$
- $-\frac{1}{2}$
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]
Asked in: MHT CET 2021 (23 Sep Shift 2)
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