limx→0+ sin⁡xsin⁡x is equal to

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

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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