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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Limits

NDA 2012 · Mathematics · Limits

What is _ x arrow 0 (2(1- x))/(x^2) equal to?

What is lim⁡x→02(1−cos⁡x)x2\lim _{x \rightarrow 0} \frac{2(1-\cos x)}{x^2} equal to?

Options

  1. A0
  2. B12\frac{1}{2}
  3. C14\frac{1}{4}
  4. D1

Correct answer

D. 1

Step-by-step solution

lim⁡x→02(1−cos⁡x)x2=lim⁡x→02×2sin⁡2x/2x2=lim⁡x→0\lim _{x \rightarrow 0} \frac{2(1-\cos x)}{x^2}=\lim _{x \rightarrow 0} \frac{2 \times 2 \sin ^2 x / 2}{x^2}=\lim _{x \rightarrow 0}\left(\frac{\sin x / 2}{x / 2}\right)^2=1
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