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MHT CET202620 April 2026Morning ShiftMathematicsLimitsActual

_ x 0 [ x (1 + 4x) (e^ 4x - 1 )^2 ] =

Options

  1. A1 4
  2. B1 16
  3. C1 3
  4. D1 9

Correct answer

A. 1 4

Step-by-step solution

_ x 0 [ x (1 + 4x) (e^ 4x - 1 )^2 ] Multiplying and dividing by appropriate powers of 4x : = _ x 0 [ x (1 + 4x) 4x 4x ( e^ 4x - 1 4x 4x )^2 ] = _ x 0 [ 4x^2 (1 + 4x) 4x 16x^2 ( e^ 4x - 1 4x )^2 ] = 4 16 _ x 0 (1 + 4x) 4x ( _ x 0 e^ 4x - 1 4x )^2 Using the standard limits _ u 0 (1 + u) u = 1 and _ u 0 e^u - 1 u = 1 : = 1 4 1 (1)^2 = 1 4 Answer: 1 4

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