AP EAMCET · Maths · Limits
\(\lim _{x \rightarrow \frac{\pi}{4}} \frac{2 \sqrt{2}-(\cos x+\sin x)^3}{1-\sin 2 x}=\)
- A \(\frac{1}{\sqrt{2}}\)
- B \(\frac{3}{2}\)
- C \(\frac{3}{\sqrt{2}}\)
- D \(\frac{\sqrt{3}}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{3}{\sqrt{2}}\)
Step-by-step Solution
Detailed explanation
\( \lim _{x \rightarrow \frac{\pi}{4}} \frac{2 \sqrt{2}-(\cos x+\sin x)^3}{1-\sin 2 x} \) Form: \( \frac{0}{0} \) Apply L'Hôpital's Rule: \( = \lim _{x \rightarrow \frac{\pi}{4}} \frac{\frac{d}{dx}(2 \sqrt{2}-(\cos x+\sin x)^3)}{\frac{d}{dx}(1-\sin 2 x)} \)…
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