Let $f:(0,1) \rightarrow R$ be the functions defined as $f(x)=\sqrt{n}$ if $x \in\left[\frac{1}{n+1}, \frac{1}{n}\right)$ where $n \in N$. Let $g :(0,1) \rightarrow R$ be a function such that $\int_{x^2}^x \sqrt{\frac{1-t}{t}}d t

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Let $f:(0,1) \rightarrow R$ be the functions defined as $f(x)=\sqrt{n}$ if $x \in\left[\frac{1}{n+1}, \frac{1}{n}\right)$ where $n \in N$. Let $g :(0,1) \rightarrow R$ be a function such that $\int_{x^2}^x \sqrt{\frac{1-t}{t}}d t<g(x)<2 \sqrt{x}$ for all $x$ $\in(0,1)$. Then $\lim _{x \rightarrow 0} f(x) g(x)$ [JEE Advanced 2023]

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Let \(f:(0,1) \rightarrow R\) be the functions defined as \(f(x)=\sqrt{n}\) if \(x \in\left[\frac{1}{n+1}, \frac{1}{n}\r…

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