MHT CET · Maths · Limits
\(\lim _{x \rightarrow 1}(\log e x)^{1 / \log x}\) is equal to
- A \(e^{-1}\)
- B \(e\)
- C \(e^{2}\)
- D 0
Answer & Solution
Correct Answer
(B) \(e\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \lim _{x \rightarrow 1}(\log e x)^{1 / \log x} &=\lim _{x \rightarrow 1}[\log e+\log x]^{1 / \log x} \\ &=\lim _{x \rightarrow 1}[1+\log x]^{1 / \log x} \\ &=e^{\lim _{x \rightarrow 1} \frac{\log x}{\log x}}=e \end{aligned}\)
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