Let denote the fractional part of x and f(x)=(cos ⁻¹(1- \²) sin ⁻¹(1- \))/(\- \³), x ≠ 0. If L and R respectively denotes the left hand limit and the right hand limit of f(x) at x=0, then 32/(π²)(~L²+R²) is equal to _ _ _ _ _ _.

Limit, Continuity and Differentiability: JEE Main 2024 Mathematics question

JEE Main 2024 · 1 Feb, Morning shift · Q42

JEE Main 20241 Feb, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let

\{x\}

denote the fractional part of

x

and

f(x)=\frac{\cos ^{-1}\left(1-\{x\}^2\right) \sin ^{-1}(1-\{x\})}{\{x\}-\{x\}^3}, x \neq 0

. If

\mathrm{L}

and

\mathrm{R}

respectively denotes the left hand limit and the right hand limit of

f(x)

x=0

, then

\frac{32}{\pi^2}\left(\mathrm{~L}^2+\mathrm{R}^2\right)

is equal to ___________.

Your answerType your answer. Integers and decimals are accepted.