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Black Book Advanced Problems in MathematicsMathematicsLimits

[ ] represents greatest integer function : array |l|l| Column-I & Column-II (A) If f(x) = ⁻¹ x and _ x 1 2 ^+ f(3x - 4x^3) = a - 3 _ x 1 2 ^- f(x), then [a] = & (P) 2 (B) If f(x) = ⁻¹ g(x) where g(x) = 3x - x^3 1 - 3x^2 and then find [ _ h 0 f ( 1 2 + 6h ) - f ( 1 2 ) 6h ] = & (Q) 3 (C) If ⁻¹ (4x^3 - 3x) = a + b ⁻¹ x for -1 < x < -1 2 , then [a + b + 2] = & (R) 4 (D) If f(x) = ⁻¹ (4x^3 - 3x) and _ x 1 2 ^+ f'(x) = a

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