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Question: \(\lim _ { x \rightarrow 0 }\) \(\frac{\sqrt{1 - \cos x^{2}}}{(1 - \cos x)}\)equals –...

lim⁡x→0\lim _ { x \rightarrow 0 } 1−cos⁡x2(1−cos⁡x)\frac{\sqrt{1 - \cos x^{2}}}{(1 - \cos x)}equals –

A

2\sqrt{2}

B

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

C

1

D

None of these

Answer

2\sqrt{2}

Explanation

Solution

lim⁡x→0\lim_{x \rightarrow 0} 1−1+x42!.....1−1+x22!.....\frac{\sqrt{1 - 1 + \frac{x^{4}}{2!}.....}}{1 - 1 + \frac{x^{2}}{2!}.....} = 2\sqrt{2}