AP EAMCET · Maths · Limits
\(\lim _{x \rightarrow \infty}\left(\frac{3 x^2-2 x+3}{3 x^2+x-2}\right)^{3 x-2}=\)
- A \(-3\)
- B \(e^{-1}\)
- C \(e^{-3}\)
- D \(-1\)
Answer & Solution
Correct Answer
(C) \(e^{-3}\)
Step-by-step Solution
Detailed explanation
Since, \(\lim _{x \rightarrow \infty}\left(\frac{3 x^2-2 x+3}{3 x^2+x-2}\right)^{3 x-2}\) \(=\lim _{x \rightarrow \infty}\left(1+\frac{(-3 x+5)}{3 x^2+x-2}\right)^{3 x-2} \quad(\because 1^\infty\) forms)…
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