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NDA 2023 Maths · Mathematics · Limits · medium

Lim x→4(√ x-2)/(x-4) is equal to

Single correct option

lim⁡x→4x−2x−4\displaystyle\lim_{x\to4}\dfrac{\sqrt x-2}{x-4} is equal to
  1. A. 12\dfrac12
  2. B. 00
  3. C. 14\dfrac14
  4. D. 44
Show answer and solution

Answer: (C) 14\dfrac14

Since x−4=(x−2)(x+2)x-4=(\sqrt x-2)(\sqrt x+2), the expression equals 1x+2→14\dfrac1{\sqrt x+2}\to\dfrac14. The value 12\dfrac12 is 124⋅2\dfrac{1}{2\sqrt4}\cdot2 from a slip in the derivative of x\sqrt x (which is 12x=14\dfrac1{2\sqrt x}=\dfrac14 at 44).
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Original question written in the NDA 2023 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake