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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Limits

NDA 2018 · Mathematics · Limits

What is _ θ arrow 0 1- θ θ equal to?

What is lim⁡θ→01−cos⁡θθ\lim _{\theta \rightarrow 0} \frac{\sqrt{1-\cos \theta}}{\theta} equal to?

Options

  1. A2\sqrt{2}
  2. B222 \sqrt{2}
  3. C12\frac{1}{\sqrt{2}}
  4. D−122-\frac{1}{2 \sqrt{2}}

Correct answer

C. 12\frac{1}{\sqrt{2}}

Step-by-step solution

lim⁡θ→01−cos⁡θθ=lim⁡θ→02sin⁡(θ/2)θ=22=12\begin{aligned} & \lim _{\theta \rightarrow 0} \frac{\sqrt{1-\cos \theta}}{\theta}=\lim _{\theta \rightarrow 0} \frac{\sqrt{2} \sin (\theta / 2)}{\theta} \\ & =\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}}\end{aligned}
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