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Question 240007
JEE Mathematics · Medium

Limits and Continuity: Factoring MCQ

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FactoringMediumQuestion 240007

Question

lim(x→3) (x³ − 27)/(x − 3) equals:
  1. A
    27
    Correct
  2. B
    9
  3. C
    3
  4. D
    0

Correct answer

27

Explanation

Using the identity aⁿ − bⁿ = (a−b)(aⁿ⁻¹ + aⁿ⁻²b + ... + bⁿ⁻¹): x³ − 27 = (x−3)(x² + 3x + 9). Cancel (x−3): limit = x² + 3x + 9 at x = 3 = 9 + 9 + 9 = 27.

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