Q229 / 270 · NDA 2018 (Phase 2) · Mathematics

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

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

Solution

$\begin{aligned} & \lim _{\theta \rightarrow 0} \frac{\sqrt{1-\cos \theta}}{\theta}=\lim _{\theta \rightarrow 0} \frac{\sqrt{2} \sin (\theta / 2)}{\theta} \\ & =\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}}\end{aligned}$

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

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