$\lim _{x \rightarrow 2}\left(\frac{5 x-8}{8-3 x}\right)^{\frac{3}{2 x-4}}=$

$\lim _{x \rightarrow 2}\left(\frac{5 x-8}{8-3 x}\right)^{\frac{3}{2 x-4}}=$
  1. $e^{5 / 2}$
  2. $\mathrm{e}^{3 / 2}$
  3. $\mathrm{e}^2$
  4. $\mathrm{e}^6$

Solution

$\begin{aligned} & \lim _{x \rightarrow 2}\left(\frac{5 x-8}{8-3 x}\right) \frac{3}{2 x-4}=e^{\lim _{x \rightarrow 2}\left(\frac{5 x-8}{8-3 x}-1\right) \times \frac{3}{2 x-4}} \\ & =e^{\lim _{x \rightarrow 2} \frac{8(x-2) \times 3}{(8-3 x) 2(x-2)}}=e^6 \\ & \end{aligned}$

Asked in: MHT CET 2022 (10 Aug Shift 1)

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