TS EAMCET · Maths · Limits
\(\lim _{x \rightarrow \infty}\left(\frac{x+5}{x+2}\right)^{x+3}\) equals
- A \(e\)
- B \(e^2\)
- C \(e^3\)
- D \(e^5\)
Answer & Solution
Correct Answer
(C) \(e^3\)
Step-by-step Solution
Detailed explanation
\(\begin{gathered}\lim _{x \rightarrow \infty}\left(\frac{x+5}{x+2}\right)^{x+3}=\lim _{x \rightarrow \infty}\left(1+\frac{3}{x+2}\right)^{x+3} \\ =\lim _{x \rightarrow \infty}\left[\left(1+\frac{3}{x+2}\right)^{\frac{x+2}{3}}\right]^{\frac{3(x+3)}{x+2}}\end{gathered}\)…
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