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Limits Continuity and Differentiability question

2025 · Shift 1 · Q27

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PYQ Library
JEE Advanced
Mathematics
Limits Continuity and Differentiability
2025 · Shift 1 · Q27

Limits Continuity and Differentiability question

2025 · Shift 1 · Q27

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityNumerical+4 / −1

Let α and β be the real numbers such that

\lim\limits_{x \to 0} \frac{1}{x^3} \left( \frac{\alpha}{2} \int\limits_0^x \frac{1}{1-t^2} \, dt + \beta x \cos x \right) = 2.

Then the value of α + β is

\underline{\hspace{2cm}}

.

Numerical answer

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