Q211 / 270 · NDA 2012 (Phase 2) · Mathematics

What is $\lim _{x \rightarrow 0} \frac{\sqrt{1+x}-1}{x}$ equal to?

  • A
    0
  • Correct answer
    B
    $\frac{1}{2}$
  • C
    1
  • D
    $-\frac{1}{2}$

Solution

$\lim _{x \rightarrow 0} \frac{\sqrt{1+x}-1}{x} \times \frac{\sqrt{1+x}+1}{\sqrt{1+x}+1}$ $=\lim _{x \rightarrow 0} \frac{1+x-1}{x(\sqrt{1+x}+1)}=\frac{x}{x(\sqrt{1+x}+1)}=\frac{1}{2}$.

Hence, the correct answer is option: 'B'.

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