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JEE Main2018MathematicsLimitsActual

lim x → 0 ( 27 + x ) 1 3 - 3 9 - ( 27 + x ) 2 3 equals

Options

  1. A- 1 6
  2. B  1 6
  3. C  1 3
  4. D- 1 3

Correct answer

A. - 1 6

Step-by-step solution

Given limit is lim x → 0 27 + x 1 3 - 3   9 - 27 + x 2 3       0 0   f o r m Applying L'Hospital's rule, ⇒ l i m x → 0   1 3 27 + x - 2 3   - 2 3 27 + x - 1 3 = 27 - 2 3 - 2 27 - 1 3 = - 1 2 27 1 3   = - 1 6 .

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