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UPSC NDA II 2023 Mathematics Solved Paper

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Consider the following for the next two (02) items that follow :

Let

f(x)=\;\frac{a^{x-1}+b^{x-1}}{2}

and

g(x)=x-1

[NDA II 2023]

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Question : 54 of 120

Marks: +1, -0

What is

\lim\limits_{x \rightarrow 1} f(x)^{\frac{1}{g(x)}}

$\sqrt{ab}$
$ab$
$2ab$
$\frac{\sqrt{ab}}{2}$

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