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Question: Answered & Verified by Expert
$\lim _{x \rightarrow \infty}\left[\frac{8 x^2+5 x+3}{2 x^2-7 x-5}\right]^{\frac{4 x+3}{8 x-1}}=$
MathematicsLimitsMHT CETMHT CET 2022 (11 Aug Shift 1)
Options:
  • A 4
  • B $\frac{1}{2}$
  • C 2
  • D $\sqrt{2}$
Solution:
2421 Upvotes Verified Answer
The correct answer is: 2
$\begin{aligned} & \lim _{x \rightarrow \infty}\left(\frac{8 x^2+5 x+3}{2 x^2-7 x-5}\right)^{\frac{4 x+3}{8 x-1}}=\lim _{x \rightarrow \infty}\left(\frac{8+\frac{5}{x}+\frac{3}{x^2}}{2-\frac{7}{x}-\frac{5}{x}}\right)^{\frac{4+\frac{3}{x}}{8-\frac{1}{x}}}=\left(\frac{8+0+0}{2-0-0}\right)^{\frac{4+0}{8-0}} \\ & =4^{\frac{1}{2}}=2\end{aligned}$

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