First slide

Introduction to limits

Question

$lim_{x \to 0^{+}} \frac{\sin \sqrt{x}}{\sqrt{\sin x}}$ is equal to

Moderate

A

0
B

1
C

-1
D

none of these

Solution

We have,
$lim_{x \to 0^{+}} \frac{\sin \sqrt{x}}{\sqrt{\sin x}} = lim_{x \to 0^{+}} \frac{\sin \sqrt{x}}{\sqrt{\frac{\sin x}{x}}} = \frac{1}{1} = 1 .$

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