If `lim_( xto 0) [(m "sin" x)/(x)] = 8` then the value of m is ([.] in the greatest integer function).

Answer

To solve the problem, we need to find the value of \( m \) such that

\[ \lim_{x \to 0} \left( m \cdot \frac{\sin x}{x} \right) = 8 \]

### Step-by-Step Solution:

1. **Understanding the limit**:
We know from the standard limit that:
\[ \lim_{x \to 0} \frac{\sin x}{x} = 1 \]
Therefore, we can rewrite the limit as:
\[ \lim_{x \to 0} \left( m \cdot \frac{\sin x}{x} \right) = m \cdot \lim_{x \to 0} \frac{\sin x}{x} = m \cdot 1 = m \]

2. **Setting up the equation**:
Given that the limit equals 8, we can set up the equation:
\[ m = 8 \]

3. **Applying the greatest integer function**:
The problem states that \( m \) is in the greatest integer function. The greatest integer function, denoted as \( \lfloor m \rfloor \), gives the largest integer less than or equal to \( m \). Since \( m = 8 \), we have:
\[ \lfloor m \rfloor = \lfloor 8 \rfloor = 8 \]

4. **Conclusion**:
Thus, the value of \( m \) in the greatest integer function is:
\[ \lfloor m \rfloor = 8 \]

### Final Answer:
The value of \( m \) is \( 8 \).