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Limits and Derivatives · JEE Preparation Mathematics

Evaluate lim{xto 0}frac{sqrt{1+2x}-sqrt{1-2x}}{x}.

Practice question from Limits and Derivatives (JEE Preparation Mathematics), with the correct answer and a step-by-step solution.

hard · MCQ · Q-B79CB5

Evaluate lim⁡x→01+2x−1−2xx\lim_{x\to 0}\frac{\sqrt{1+2x}-\sqrt{1-2x}}{x}.

  1. A.0
  2. B.1
  3. C.2Correct answer
  4. D.4

Solution

Rationalising the numerator gives (1+2x)−(1−2x)x(1+2x+1−2x)=41+2x+1−2x\frac{(1+2x)-(1-2x)}{x(\sqrt{1+2x}+\sqrt{1-2x})}=\frac{4}{\sqrt{1+2x}+\sqrt{1-2x}}. As x→0x\to 0, the value approaches 42=2\frac{4}{2}=2.

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