CUET · MATHS · PYQ PAPER 2023
\(\lim _{x \rightarrow \infty}\left(\frac{x+7}{x+1}\right)^x\) is equal to:
- A \(e\)
- B \(e^3\)
- C \(e^6\)
- D \(e^7\)
Answer & Solution
Correct Answer
(C) \(e^6\)
Step-by-step Solution
Detailed explanation
\( \lim _{x \rightarrow \infty}\left(\frac{x+7}{x+1}\right)^x = e^{\lim_{x \rightarrow \infty} x \left( \frac{x+7}{x+1} - 1 \right)} \) \( = e^{\lim_{x \rightarrow \infty} x \left( \frac{x+7-x-1}{x+1} \right)} \)…
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