Let f:(0,1) → R be the function defined as f(x) = √(n) if x ∈ [1/(n+1), 1/n ) where n ∈ N. Let g:(0,1) → R be a function such that displaystyleint_x^2^x √((1-t)/t) dt < g(x) < 2√(x) for all x ∈ (0,1). Then displaystylelim_x → 0 f(x)g(x)

Let f:(0,1) → R be the function defined as f(x) = √(n) if x… — JEE Advanced 2023 Mathematics PYQ

JEE Advanced 2023 · Paper 1

Let

f:(0,1) \to \mathbb{R}

be the function defined as

f(x) = \sqrt{n}

x \in \left[\dfrac{1}{n+1}, \dfrac{1}{n}\right)

where

n \in \mathbb{N}

. Let

g:(0,1) \to \mathbb{R}

be a function such that

\displaystyle\int_{x^2}^{x} \sqrt{\dfrac{1-t}{t}}\,dt < g(x) < 2\sqrt{x}

for all

x \in (0,1)

. Then

\displaystyle\lim_{x \to 0} f(x)g(x)

Show answer

Correct option: C

[JEE Advanced 2023 · Paper 1]

Practise Limits Continuity and Differentiability the way it is asked

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