Find `lim_(xto0) sqrt((1)/(2)(1-cos2x))/(x)` if exists.

Explanation

To solve the limit \( \lim_{x \to 0} \frac{\sqrt{\frac{1}{2}(1 - \cos 2x)}}{x} \), we can follow these steps:

### Step 1: Simplify the expression inside the limit
We start with the expression:
\[ \frac{\sqrt{\frac{1}{2}(1 - \cos 2x)}}{x} \]
Using the trigonometric identity \( 1 - \cos 2x = 2 \sin^2 x \), we can rewrite the expression:
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