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