First slide

Introduction to limits

Question

$lim_{x \to \infty} {(1 - \frac{4}{x - 1})}^{3 x - 1}$ is equal to

Moderate

A

$e^{12}$
B

$e^{- 12}$
C

$e^{4}$
D

$e^{3}$

Solution

We have to find
$lim_{x \to \infty} {(1 - \frac{4}{x - 1})}^{3 x - 1}$
$= lim_{x \to \infty} {(1 + \frac{(- 4)}{x - 1})}^{3 x - 1} = e^{{lim}_{x \to \infty}^{} - 4 \frac{(3 x - 1)}{x - 1}} = e^{- 12}$

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