JEE Mains · Maths · STD 11 - 12. limits
\(\lim _{x \rightarrow \frac{\pi}{4}} \frac{8 \sqrt{2}-(\cos x+\sin x)^{7}}{\sqrt{2}-\sqrt{2} \sin 2 x}\) is equal to
- A \(14\)
- B \(7\)
- C \(14 \sqrt{2}\)
- D \(7 \sqrt{2}\)
Answer & Solution
Correct Answer
(A) \(14\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow \frac{\pi}{4}} \frac{8 \sqrt{2}-(\cos x+\sin x)^{7}}{\sqrt{2}-\sqrt{2} \sin 2 x} \quad\left(\frac{0}{0}\right.\) form \()\) \(=\lim _{x \rightarrow \frac{\pi}{4}} \frac{-7(\cos x+\sin x)^{6}(-\sin x+\cos x)}{-2 \sqrt{2} \cos 2 x}\) using \(L-H\)…
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