https://file.aiquickdraw.com/mathbot/file/1730224511551rvdmvqi8.jpg

To estimate \(\lim_{x \to 1^+} g(x)\) using the graph, let's examine the behavior of \(g(x)\) as \(x\) approaches \(1\) from the right side (values slightly greater than 1).

1. **Identify the right-hand limit:** Look at the values of \(g(x)\) as \(x\) approaches \(1\) from values slightly greater than \(1\).
   
2. **Determine the approximate \(y\)-value:** Following the graph as \(x \to 1^+\), we see that \(g(x)\) approaches the value \(2\). 

### Conclusion
Therefore, based on the graph, we can estimate:
\[
\lim_{x \to 1^+} g(x) = 2.
\]

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

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Here are 5 related questions for deeper understanding:

1. What is the difference between a right-hand limit and a left-hand limit?
2. How would the answer change if we were asked for \(\lim_{x \to 1^-} g(x)\)?
3. What if we needed \(\lim_{x \to 1} g(x)\) instead of just the right-hand limit?
4. How can we determine continuity at \(x = 1\) using limits?
5. Why is it important to consider limits from both sides when evaluating a general limit?

**Tip:** To find one-sided limits, always look for values slightly above or below the target \(x\)-value on the graph to see what \(y\)-value the function approaches.

Use the graph of the function g shown to estimate \( \lim_{x \to 1^+} g(x) \).

Learn how to estimate the right-hand limit \( \lim_{x \to 1^+} g(x) \) using a graph. This example covers key calculus concepts, including limits and one-sided limits, and guides students in interpreting function behavior from a graph. Suitable for Grades 11-12.

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