The image shows a mathematics worksheet focusing on limits and limit theorems. Below are the problems given in the worksheet:

1. $\lim_{{x \to 1}} (6x^2 + 8x)$
2. $\lim_{{x \to 2}} \frac{x^2 + x - 6}{x - 2}$
3. $\lim_{{x \to 4}} \frac{x - 2}{x - 4}$
4. $\lim_{{x \to 1}} \frac{\sqrt{x} - 1}{x - 1}$

Would you like detailed step-by-step solutions for each limit? Let me know which ones you need help with!

Here are some related questions you might be interested in:

1. What are the different methods to evaluate limits?
2. How do you determine if a limit exists?
3. What is L'Hôpital's rule, and when is it used?
4. How do you evaluate limits involving square roots?
5. What are left-hand and right-hand limits?

Tip: When evaluating limits, always try direct substitution first. If it leads to an indeterminate form (like $0/0$), apply factoring, rationalization, or L'Hôpital's Rule as needed.