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To determine the limit of \( h(x) \) as \( x \) approaches \( 5 \) from the left (\( x \to 5^- \)), we need to analyze the behavior of the function \( h(x) \) as \( x \) gets closer to 5 from the left side on the graph.

Looking at the graph:
- As \( x \) approaches 5 from the left, the function \( h(x) \) approaches a value close to 2. The function doesn't show any jumps, discontinuities, or oscillations near \( x = 5^- \), so we can confidently say that:

\[
\lim_{{x \to 5^-}} h(x) = 2
\]

Would you like further explanation or have any questions about this? 

Here are five related questions to explore this topic further:
1. What is the limit of \( h(x) \) as \( x \) approaches \( 5 \) from the right (\( x \to 5^+ \))?
2. How do you find the overall limit of \( h(x) \) as \( x \) approaches 5?
3. What are the possible reasons for a limit not existing at a particular point?
4. How does the continuity of \( h(x) \) at \( x = 5 \) relate to the limits from both sides?
5. What is the significance of one-sided limits in understanding the behavior of a function at a point?

**Tip:** When analyzing limits graphically, focus on the function's behavior near the point of interest, checking both left-hand and right-hand limits to understand the function's behavior fully.

Explore the limit of h(x) as x approaches 5 from the left (x → 5⁻). Learn how to analyze the behavior of functions near specific points using limit theorems. Suitable for advanced high school and college students.

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