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It looks like you've uploaded a knowledge check from a Math 241 course focused on limits and continuity. Here's an outline of the problems based on what I see:

1. **Limits from a graph** (Various limit evaluations from a given graph).
2. **Evaluate limits analytically** (Using algebraic methods).
3. **More complex limit evaluations** (Involving specific forms like 0/0).
4. **Additional limit evaluations** (Polynomials and rational functions).
5. **Limit at negative infinity** (Evaluating a function at \( x \to -\infty \)).
6. **Conditions for continuity** (What conditions must hold at a point for continuity).
7. **Discontinuities in a graph** (Identifying where the graph is not continuous).
8. **Definition of continuity at a point** (Applying the formal definition to a piecewise function).

Would you like to work through one of these problems step by step? 

### Here are some additional questions to consider:
1. How can you determine one-sided limits from a graph?
2. What strategies can you use when faced with indeterminate forms like 0/0?
3. What is the definition of continuity at a point?
4. How do you evaluate limits as \( x \to \infty \) or \( x \to -\infty \)?
5. What role do removable discontinuities play in continuity?

**Tip**: When evaluating limits, always check if you can simplify the function before substituting the limit value. This can help avoid indeterminate forms!

Math 241-001 Knowledge Check 1 (Fall 2024) involving limits and continuity. Specific problems ask for the evaluation of limits from graphs, the use of algebraic methods to solve limits, the definition and conditions for continuity, and the identification of discontinuities in a graph.

Explore a detailed knowledge check for Math 241, covering limit evaluations from graphs, algebraic solutions for limits, and understanding continuity conditions. This check includes real-world problems and solutions for students in Calculus I.

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