First slide

Introduction to limits

Question

$lim_{x \to \infty} {(\frac{x + 2}{x + 1})}^{x + 3}$ is equal to

Moderate

A

1
B

e
C

$e^{2}$
D

$e^{3}$

Solution

We have,
$lim_{x \to \infty} {(\frac{x + 2}{x + 1})}^{x + 3} = lim_{x \to \infty} {(1 + \frac{1}{x + 1})}^{x + 3} = e^{lim_{x \to \infty} \frac{x + 3}{x + 1}} = e$

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