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JEE Main20249 Apr 2024Evening ShiftMathematicsLimitsActual

_ x 0 e-(1+2 x)^ 1 2 x x is equal to

Options

  1. A0
  2. B-2 e
  3. Ce
  4. De-e^2

Correct answer

C. e

Step-by-step solution

aligned & Lim _ x 0 e-e^ 1 2 x (1+2 x) x & = Lim _ x 0 (-e) (e^ (1+2 x) 2 x -1 -1 ) x & = Lim _ x 0 (-e) (1+2 x)-2 x 2 x^2 & =(-e) (-1) 4 2 2 =e aligned

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