First slide

Introduction to limits

Question

The value of $lim_{x \to \infty} {(\frac{x + 3}{x - 1})}^{x + 3}$ is

Moderate

A

$e$
B

$e^{2}$
C

$e^{4}$
D

$1 / e$

Solution

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

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