Function f(x) = {x^{frac{1}{{ln ,x}}}}

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1.Relation and Function

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The function $f(x) =$ ${x^{\frac{1}{{\ln \,x}}}}$

A

is a constant function

B

has a domain $(0, 1) U (e, \infty )$

C

is such that $\mathop {\lim it}\limits_{x \to 1} f(x) $ exist

D

$(A)$ or $(C)$ both

Solution

$y = x{\log _x}e$ $= e$ (constant)

$\Rightarrow A$ and $C$

as $\mathop {\lim it}\limits_{x \to 1} $ $f(x) = e$

Standard 12

Mathematics

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