AP EAMCET · Maths · Limits
\(\lim _{x \rightarrow \infty}[x-\log (\cosh x)]=\)
- A \(2\)
- B \(0\)
- C \(\log \frac{1}{2}\)
- D \(\log 2\)
Answer & Solution
Correct Answer
(D) \(\log 2\)
Step-by-step Solution
Detailed explanation
\( \lim _{x \rightarrow \infty}[x-\log (\cosh x)] \) \( = \lim _{x \rightarrow \infty}\left[x-\log \left(\frac{e^x+e^{-x}}{2}\right)\right] \) \( = \lim _{x \rightarrow \infty}\left[x-\log \left(\frac{e^x(1+e^{-2x})}{2}\right)\right] \)…
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