Q116 / 180 · COMEDK 2013 · Mathematics

$\lim _{x \rightarrow \infty}\left(1-\frac{4}{x-1}\right)^{3 x-1}$ is equal to

  • A
    $e^{12}$
  • Correct answer
    B
    $e^{-12}$
  • C
    $e^{4}$
  • D
    $e^{3}$

Solution

$\begin{aligned} \lim _{x \rightarrow \infty}(1-&\left.\frac{4}{x-1}\right)^{3 x-1} \\ &=e^{\lim _{x \rightarrow \infty}}\left(\frac{-4}{x-1}\right)\left(1^{\infty} \text { form] }\right.\\ &=e^{\lim _{x \rightarrow \infty}-\frac{12 x+4}{x-1}}=e^{-12} \end{aligned}$

Hence, the correct answer is option: 'B'.

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