https://file.aiquickdraw.com/mathbot/file/1727279613539jw7gwzn9.jpg

The expression in the image is:

\[
\lim_{{t \to 3^-}} \sqrt{3 - t}
\]

This represents the limit of the square root of \(3 - t\) as \(t\) approaches 3 from the left (\(t \to 3^-\)).

### Analysis:

1. As \(t\) approaches 3 from the left, \(t\) is slightly less than 3. Thus, \(3 - t\) is a small positive number.
   
2. Since the square root function is defined for non-negative numbers, we must ensure that \(3 - t \geq 0\), which holds true as long as \(t \leq 3\).

3. When \(t\) gets very close to 3 from the left, \(3 - t\) approaches 0, and the square root of 0 is 0.

### Conclusion:
\[
\lim_{{t \to 3^-}} \sqrt{3 - t} = 0
\]

Let me know if you'd like more details or have any questions.

### Related Questions:
1. What happens to the limit as \(t\) approaches 3 from the right (\(t \to 3^+\))?
2. How would this limit change if it were \(\lim_{{t \to 0^+}} \sqrt{3 - t}\)?
3. How can limits involving square roots be evaluated when the input approaches a negative number?
4. What is the geometric interpretation of the limit approaching from the left for this function?
5. How does this limit behave in the context of continuity of the function \(\sqrt{3 - t}\)?

### Tip:
Always consider whether the function is defined in the neighborhood of the point you're approaching, especially for square roots and logarithmic functions.

Learn how to evaluate the limit lim (t -> 3^-) sqrt(3 - t) with detailed steps and analysis. Understand how the function behaves as t approaches 3 from the left, and why the result is 0. Suitable for high school students studying calculus.

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