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MHT CET202519 Apr 2025Morning ShiftMathematicsLimitsActual

_ x 3 (84-x)^ 1 4 -3 x-3 is

Options

  1. A-1 108
  2. B-1 84
  3. C-1 27
  4. D-1 4

Correct answer

A. -1 108

Step-by-step solution

Evaluating _ x 3 (84-x)^ 1 4 -3 x-3 by substitution gives the indeterminate form 0 0 , so we apply L'Hôpital's Rule. Differentiating numerator and denominator: f(x) = (84-x)^ 1 4 -3 f'(x) = - 1 4 (84-x)^ - 3 4 g(x) = x-3 g'(x) = 1 The limit becomes: _ x 3 - 1 4 (84-x)^ - 3 4 1 = - 1 4 (81)^ - 3 4 Simplifying through exponent rules: - 1 4 (3^4)^ - 3 4 = - 1 4 3⁻³ = - 1 4 1 27 = - 1 108 Final answer: - 1 108

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