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The given function \( f(x) \) is a piecewise function defined as follows:

\[
f(x) = \begin{cases} 
x + 5 & \text{if } x < -2, \\
5 & \text{if } x > -2.
\end{cases}
\]

You are asking for the limit of \( f(x) \) as \( x \to -2^- \), which means from the left-hand side of \( -2 \).

For values of \( x \) approaching \( -2 \) from the left (i.e., \( x < -2 \)), the function follows the rule \( f(x) = x + 5 \).

Thus, we compute the left-hand limit:

\[
\lim_{x \to -2^-} f(x) = \lim_{x \to -2^-} (x + 5) = -2 + 5 = 3.
\]

Therefore, the limit as \( x \to -2^- \) is:

\[
\lim_{x \to -2^-} f(x) = 3.
\]

Would you like further details on this, or do you have any questions?

### Related Questions:
1. What is the right-hand limit \( \lim_{x \to -2^+} f(x) \)?
2. Is \( f(x) \) continuous at \( x = -2 \)?
3. How do we find the overall limit of a piecewise function at a given point?
4. How do limits relate to the continuity of functions?
5. Can the function \( f(x) \) be differentiable at \( x = -2 \)?

### Tip:
When dealing with piecewise functions, always check the conditions for each piece and evaluate the limits from both sides to understand behavior around a given point.

Find the limit of the piecewise function f(x) as x approaches -2 from the left-hand side. This problem explains the process of calculating limits for piecewise functions, ideal for students in grades 10-12.

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