https://file.aiquickdraw.com/mathbot/file/1725418832856lq23wgpi.pdf

The file you uploaded is a Calculus I quiz, covering sections 1.1-1.3. It includes various problems on limits, continuity, and the Intermediate Value Theorem. Here's a breakdown of the problems:

1. **Limits from a Graph**: The first set of questions asks to determine the limits based on the graph of a function \( f(x) \), including whether the limits exist or not.
2. **Evaluating Limits**: The second set involves finding limits of functions algebraically, with instructions not to use L'Hôpital's rule.
3. **Continuity and Discontinuity**: There are questions on determining whether a function is continuous on a given interval and identifying removable or non-removable discontinuities.
4. **Intermediate Value Theorem**: The quiz also asks to verify that a given function has a zero in a specified interval using the Intermediate Value Theorem.

Would you like to work through any specific problems, or would you like a detailed explanation of any of these concepts?

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**Related Questions:**
1. How do you determine the limit of a function as \( x \) approaches a specific value?
2. What are the conditions for a function to be continuous at a point?
3. How can you identify if a discontinuity is removable or non-removable?
4. What is the Intermediate Value Theorem, and how is it applied to prove the existence of zeros?
5. How do you algebraically solve limits that involve square roots or polynomial expressions?

**Tip:** When solving limits, it’s often helpful to first try direct substitution. If that results in an indeterminate form like \( \frac{0}{0} \), you might need to factor or rationalize the expression.

The file you uploaded is a Calculus I quiz, covering sections 1.1-1.3. It includes various problems on limits, continuity, and the Intermediate Value Theorem.

Explore a comprehensive Calculus I quiz covering key topics such as limits, continuity, discontinuities, and the Intermediate Value Theorem. This quiz is designed for undergraduate students to practice and reinforce their understanding of these foundational concepts.

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