Question

$ \lim\limits _{x\to 1 } \left(log \,ex\right)^{1/log\,x} $ is equal

• A. $ e^{-1} $
• B. $ e $
• C. $ e^2 $
• D. $ 0 $

Answer 1

Answer: (B)

$ \displaystyle\lim _{x \rightarrow 1}(\log e x)^{1 / \log x}=\displaystyle\lim _{x \rightarrow 1}[\log e+\log x]^{1 / \log x} $
$= \displaystyle\lim _{x \rightarrow 1}[1+\log x]^{1 / \log x} $
$=e^{\displaystyle\lim _{x \rightarrow 1} \frac{\log x}{\log x}}=e$