Q10. Use the provided graph to find the following. If a limit or function value does not exist, write DNE and explain why it does not exist.

Background

Topic: Limits and Continuity

This question tests your understanding of how to evaluate limits and function values from a graph, as well as how to determine continuity at a point.

Key Terms and Concepts:

• Limit: The value that a function approaches as the input approaches a certain value.

• One-sided limits: The value the function approaches from the left () or right ().

• Function value: The actual value of at a specific .

• Continuity: A function is continuous at if and the limit exists.

Step-by-Step Guidance

1. For each limit, identify the -value in question and examine the graph as approaches that value from the left and right.

2. For one-sided limits (e.g., ), look only at the behavior as approaches from the specified side.

3. For , find the filled (solid) dot at on the graph. The -value of this point is .

4. For continuity at , check three things: (1) exists, (2) exists, and (3) these two values are equal.

5. If a limit does not exist (DNE), look for jumps, holes, or asymptotes at that -value and be ready to explain why.

Try solving on your own before revealing the answer!