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Limits Continuity and Differentiability question

2025 · 29 Jan · Shift 1 · Q46

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JEE Main
Mathematics
Limits Continuity and Differentiability
2025 · 29 Jan · Shift 1 · Q46

Limits Continuity and Differentiability question

2025 · 29 Jan · Shift 1 · Q46

JEE MainMathematicsLimits Continuity and DifferentiabilityNumerical+4 / −1

Let [t] be the greatest integer less than or equal to t. Then the least value of p ∈ N for which

\lim\limits_{x \to 0^+} \left( x (\left[ \frac{1}{x} \right] + \left[ \frac{2}{x} \right] + \ldots + \left[ \frac{p}{x} \right] \right) - x^2 \left( \left[ \frac{1}{x^2} \right] + \left[ \frac{2^2}{x^2} \right] + \ldots + \left[ \frac{9^2}{x^2} \right] \right) \geq 1

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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