COMEDK · Maths · 16. Limits
\(\lim _{x \rightarrow 0} \dfrac{\sqrt{1-\cos 2 x}}{x \sqrt{2}}\)
- A is equal to -1
- B is equal to 1
- C is equal to 0
- D does not exist
Answer & Solution
Correct Answer
(D) does not exist
Step-by-step Solution
Detailed explanation
The given limit is \(L = \lim _{x \rightarrow 0} \dfrac{\sqrt{1-\cos 2 x}}{x \sqrt{2}}\). Using the trigonometric identity \(1 - \cos 2x = 2 \sin^2 x\), we have \(\sqrt{1 - \cos 2x} = \sqrt{2 \sin^2 x} = \sqrt{2} |\sin x|\). Substituting this into the expression,…
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