If , then the value of , is Note: denotes the greatest integer less than or equal…

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

If lim⁡x→0([sin⁡−1xx]+[22sin⁡−12xx]+[32sin⁡−13xx]+⋯+[n2sin⁡−1nxx])=100\lim_{x \rightarrow 0} \left( \left[ \frac{\sin^{-1} x}{x} \right] + \left[ \frac{2^2 \sin^{-1} 2x}{x} \right] + \left[ \frac{3^2 \sin^{-1} 3x}{x} \right] + \dots + \left[ \frac{n^2 \sin^{-1} nx}{x} \right] \right) = 100, then the value of nn, is Note: [k][k] denotes the greatest integer less than or equal to kk (a) 22 (b) 33 (c) 44 (d) 55

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