MHT CET · Maths · Limits
\(\lim _{x \rightarrow \infty}\left(\frac{x+8}{x+1}\right)^{x+5}=\ldots\)
- A \(e^4\)
- B \(\mathrm{e}^5\)
- C \(\mathrm{e}^{11}\)
- D \(\mathrm{e}^7\)
Answer & Solution
Correct Answer
(D) \(\mathrm{e}^7\)
Step-by-step Solution
Detailed explanation
\( \lim _{x \rightarrow \infty}\left(\frac{x+8}{x+1}\right)^{x+5} = \lim _{x \rightarrow \infty}\left(1 + \frac{7}{x+1}\right)^{x+5} \) \( = e^{\lim _{x \rightarrow \infty}\left(\frac{7}{x+1}\right)(x+5)} \)
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