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Limits Continuity and Differentiability question

2024 · 1 Feb · Shift 1 · Q55

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JEE Main
Mathematics
Limits Continuity and Differentiability
2024 · 1 Feb · Shift 1 · Q55

Limits Continuity and Differentiability question

2024 · 1 Feb · Shift 1 · Q55

JEE MainMathematicsLimits Continuity and DifferentiabilityNumerical+4 / −1

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 eq 0

. If

\mathrm{L}

and

\mathrm{R}

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

f(x)

at

x=0

, then

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

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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