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What is the limit of h(x) as x approaches 4

To find the limit of \( h(x) \) as \( x \) approaches 4, we need to analyze the graph you've provided near \( x = 4 \). Here's the breakdown:

- As \( x \) approaches 4 from the **left** (\( x \to 4^- \)), the graph of \( h(x) \) descends toward \( h(x) = -4 \).
- As \( x \) approaches 4 from the **right** (\( x \to 4^+ \)), the graph rises toward \( h(x) = -4 \).

Since both the left-hand and right-hand limits approach \( -4 \), we conclude that:

\[
\lim_{x \to 4} h(x) = -4
\]

Would you like more details on limit behavior or any other part of the graph explained?

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Here are 5 related questions that expand on this concept:
1. What is the limit of \( h(x) \) as \( x \) approaches 0?
2. Does the limit of \( h(x) \) exist as \( x \) approaches -6?
3. Is \( h(x) \) continuous at \( x = 4 \)? Why or why not?
4. What is the value of \( h(4) \), and how does it compare to the limit?
5. How would you determine whether \( h(x) \) is differentiable at \( x = 4 \)?

**Tip:** When determining limits from a graph, always check both the left-hand and right-hand behavior to ensure the function approaches the same value from both directions.

What is the limit of h(x) as x approaches 4?

Learn how to find the limit of h(x) as x approaches 4 by analyzing a graphical representation. Both left-hand and right-hand limits are considered to conclude that the limit is -4. Suitable for students in Grades 9-12.

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