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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Limits

NDA 2012 · Mathematics · Limits

What is _ x arrow 0 1+x -1 x equal to?

What is lim⁡x→01+x−1x\lim _{x \rightarrow 0} \frac{\sqrt{1+x}-1}{x} equal to?

Options

  1. A0
  2. B12\frac{1}{2}
  3. C1
  4. D−12-\frac{1}{2}

Correct answer

B. 12\frac{1}{2}

Step-by-step solution

lim⁡x→01+x−1x×1+x+11+x+1=lim⁡x→01+x−1x(1+x+1)=xx(1+x+1)=12\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}.
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