MHT CET · Maths · Limits
\(\lim _{x \rightarrow x}\left[\frac{\sqrt{x}-1}{\log x}\right]=\)
- A \(\frac{1}{2}\)
- B \(2\)
- C \(-2\)
- D \(-\frac{1}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(
\begin{aligned}
& \lim _{x \rightarrow x}\left[\frac{\sqrt{x}-1}{\log x}\right] \\
& =\lim _{x \rightarrow 1} \frac{\frac{1}{2 \sqrt{x}}}{\left(\frac{1}{x}\right)} \\
& =\frac{1}{2}
\end{aligned}
\)
... [L' Hospital rule]
\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]
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