MCQ
The function $f(x) =$ ${x^{\frac{1}{{\ln \,x}}}}$
- Ais a constant function
- Bhas a domain $(0, 1) U (e, \infty )$
- Cis such that $\mathop {\lim it}\limits_{x \to 1} f(x) $ exist
- ✓$(A)$ or $(C)$ both
✓
Answer
Correct option: D.
$(A)$ or $(C)$ both
d
$y = x{\log _x}e$ $= e$ (constant)
$y = x{\log _x}e$ $= e$ (constant)
$\Rightarrow A$ and $C$
as $\mathop {\lim it}\limits_{x \to 1} $ $f(x) = e$
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