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KCET2013MathematicsLimits

_ x 0 _ e (1+x) 3^ x -1 is equal to

Options

  1. A_ e 3
  2. B0
  3. C₃ e
  4. D1

Correct answer

C. ₃ e

Step-by-step solution

aligned _ x 0 _ e (1+x) 3^ x -1 ( form 0 0 ) &= _ x 0 ( 1 1+x ) 3^ x _ e 3 (use L-hospital rule) &= ( 1 1+0 ) 3⁰ _ e 3 &= 1 _ e 3 = ₃ e aligned

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