`lim_(xrarr0)(sinmxcot(x/sqrt(3)))=2`, then m=…………….

Explanation

To solve the limit problem \( \lim_{x \to 0} \left( \sin(mx) \cot\left(\frac{x}{\sqrt{3}}\right) \right) = 2 \), we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Limit Form**:
We start by substituting \( x = 0 \) into the expression. We find that both \( \sin(mx) \) and \( \cot\left(\frac{x}{\sqrt{3}}\right) \) approach 0 as \( x \to 0 \). Thus, we have a \( \frac{0}{0} \) indeterminate form.

2. **Rewrite the Expression**:
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