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The document you've uploaded contains algebraic limits problems from a differential calculus course. Here are some of the problems:

### Example Problems:
1. \(\lim_{x \to 5} \frac{x^4 - 25}{x - 5}\)
2. \(\lim_{x \to 7} \frac{x^2 - 49}{x - 7}\)
3. \(\lim_{x \to 2} \frac{x - 6}{x^3 - 2x^2}\)
4. \(\lim_{x \to 3} \frac{x^3 - 1}{x^2 - 13}\)
5. \(\lim_{x \to 3} \frac{x^3 - 2}{x^2 - 9}\)

The instructions emphasize using algebraic theorems, including factorization and rationalization, to simplify and compute the limits. Full procedures are required for credit, and results should be in fraction form, where applicable.

Would you like assistance solving any specific problems? Or should I guide you through the factorization and limit process in general?

### Expanding Concepts (Sample Questions):
1. How do you factor expressions like \(x^4 - 25\)?
2. What are the common limit properties useful for these types of problems?
3. How do you simplify limits involving indeterminate forms like \(\frac{0}{0}\)?
4. What is the role of rationalization in limit calculation?
5. How do you handle limits approaching infinity in similar problems?

### Tip:
Always check for opportunities to factor and cancel out terms before plugging in the limit value.

The document contains algebraic limits problems from a differential calculus course. Example problems include limits like \(\lim_{x \to 5} \frac{x^4 - 25}{x - 5}\), \(\lim_{x \to 7} \frac{x^2 - 49}{x - 7}\), and others involving factorization and rationalization techniques.

Learn how to solve algebraic limits like \(\lim_{x \to 5} \frac{x^4 - 25}{x - 5}\) and \(\lim_{x \to 7} \frac{x^2 - 49}{x - 7}\) by applying factorization and rationalization techniques. This guide covers key calculus concepts and provides step-by-step procedures suitable for undergraduate calculus students.

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