First slide

Introduction to limits

Question

$lim_{x \to 0} \frac{\sqrt[]{1 + x} - 1}{x}$ is equal to

Moderate

A

$\frac{1}{2}$
B

2
C

0
D

1

Solution

We have,
$lim_{x \to 0} \frac{\sqrt{1 + x} - 1}{x} = lim_{x \to 0} \frac{x}{x {\sqrt{1 + x} + 1}} = lim_{x \to 0} \frac{1}{\sqrt{1 + x} + 1} = \frac{1}{2}$

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