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AP EAMCET · Maths · Limits

\(\lim _{x \rightarrow \frac{\pi}{2}} \frac{1+\cos 2 x}{\cot 3 x\left(3^{\sin 2 x}-1\right)}=\)

  1. A \(\frac{1}{3 \log 9}\)
  2. B \(\frac{2}{3 \log 3}\)
  3. C \(\frac{1}{3 \log 3}\)
  4. D \(\frac{3}{\log 3}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{1}{3 \log 3}\)

Step-by-step Solution

Detailed explanation

\(\lim _{x \rightarrow \frac{\pi}{2}} \frac{1+\cos 2 x}{\cot 3 x\left(3^{\sin 2 x}-1\right)} \Rightarrow \lim _{x \rightarrow \frac{\pi}{2}} \frac{2 \cos ^2 x}{\frac{\cos 3 x}{\sin 3 x} \times\left(3^{\sin 2 x}-1\right)}\) Let \(x=\frac{\pi}{2}-h\), then…