Fill in the blanks in each of the followings:
`underset(xto2^(-))[x]`=_______

Answer

To solve the problem, we need to evaluate the limit of the greatest integer function (also known as the floor function) as \( x \) approaches \( 2 \) from the left (denoted as \( 2^- \)).

### Step-by-Step Solution:

1. **Understanding the Greatest Integer Function**:
The greatest integer function, denoted as \( \lfloor x \rfloor \), gives the largest integer less than or equal to \( x \). For example:
- \( \lfloor 1.3 \rfloor = 1 \)
- \( \lfloor 1.9 \rfloor = 1 \)
- \( \lfloor 2 \rfloor = 2 \)

2. **Evaluating the Limit**:
We need to find \( \lim_{x \to 2^-} \lfloor x \rfloor \). This means we are looking at values of \( x \) that are approaching \( 2 \) from the left side (values slightly less than \( 2 \)).

3. **Choosing Values**:
Let's consider some values of \( x \) approaching \( 2 \) from the left:
- If \( x = 1.9 \), then \( \lfloor 1.9 \rfloor = 1 \)
- If \( x = 1.99 \), then \( \lfloor 1.99 \rfloor = 1 \)
- If \( x = 1.999 \), then \( \lfloor 1.999 \rfloor = 1 \)

4. **Conclusion**:
As \( x \) gets closer to \( 2 \) from the left, the greatest integer function remains \( 1 \). Therefore, we conclude that:
\[ \lim_{x \to 2^-} \lfloor x \rfloor = 1 \]

### Final Answer:
\[ \underset{x \to 2^-}{\lim} \lfloor x \rfloor = 1 \]