ExamBro
ExamBro
AP EAMCET · Maths · Limits

\(\lim _{x \rightarrow \infty}[x-\log (\cosh x)]=\)

  1. A \(2\)
  2. B \(0\)
  3. C \(\log \frac{1}{2}\)
  4. D \(\log 2\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\log 2\)

Step-by-step Solution

Detailed explanation

\( \lim _{x \rightarrow \infty}[x-\log (\cosh x)] \) \( = \lim _{x \rightarrow \infty}\left[x-\log \left(\frac{e^x+e^{-x}}{2}\right)\right] \) \( = \lim _{x \rightarrow \infty}\left[x-\log \left(\frac{e^x(1+e^{-2x})}{2}\right)\right] \)…