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Question: Answered & Verified by Expert
The $\lim _{x \rightarrow \infty}\left(\frac{3 x-1}{3 x+1}\right)^{4 x}$ equals
MathematicsLimitsJEE Main
Options:
  • A 1
  • B 0
  • C $\mathrm{e}^{-8 / 3}$
  • D $\mathrm{e}^{-4 / 9}$
Solution:
2390 Upvotes Verified Answer
The correct answer is: $\mathrm{e}^{-8 / 3}$
$\lim _{x \rightarrow \infty}\left(\frac{3 x-1}{3 x+1}\right)^{4 x}=1^{\infty}=e^{L}=e^{-\frac{8}{3}}$
$L=\lim _{x \rightarrow \infty} 4 x\left(\frac{3 x-1}{3 x+1}-1\right)=\lim _{x \rightarrow \infty} 4 x\left(\frac{-2}{3 x+1}\right)=\frac{-8}{3}$

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