Evaluate `lim_(x to 0) ("sin"^(2) (3x//2x))/(x)`

Explanation

To evaluate the limit \( \lim_{x \to 0} \frac{\sin^2\left(\frac{3x}{2}\right)}{x} \), we can follow these steps:

### Step 1: Rewrite the limit
We start with the expression:
\[ \lim_{x \to 0} \frac{\sin^2\left(\frac{3x}{2}\right)}{x} \]
We can rewrite this limit to help us apply the standard limit \( \lim_{u \to 0} \frac{\sin u}{u} = 1 \).
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