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Question 240016
JEE Mathematics · Hard

Limits and Continuity: JEE Advanced MCQ

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JEE AdvancedHardQuestion 240016

Question

lim(x→0⁺) x^x equals:
  1. A
    1
    Correct
  2. B
    0
  3. C
    e
  4. D
    ∞

Correct answer

1

Explanation

Let L = lim(x→0⁺) x^x. Take ln: ln L = lim(x→0⁺) x ln x. As x → 0⁺, x → 0 and ln x → −∞, but x ln x → 0 (exponential dominates). So ln L = 0 → L = e⁰ = 1.

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