AP EAMCET · Maths · Limits
\(\lim _{x \rightarrow \infty}\left(\frac{x+6}{x+1}\right)^{x+4}\) is equal to
- A \(e^4\)
- B \(e^6\)
- C \(e^5\)
- D \(e\)
Answer & Solution
Correct Answer
(C) \(e^5\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } \lim _{x \rightarrow \infty}\left(\frac{x+6}{x+1}\right)^{x+4} \\ & \lim _{x \rightarrow \infty}\left(\frac{1+\frac{6}{x}}{1+\frac{1}{x}}\right)^{x+4} \\ & x \rightarrow \infty, 1+\frac{6}{x} \rightarrow 1,1+\frac{1}{x} \rightarrow 1 \\ & \qquad…
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