2. Limits, Asymptotes, and Continuity
Ex.
Ex.
Ex.
Ex.

3. Ex.
Ex.

4. Ex.
Ex.

5. Ex.

6. Def. A horizontal asymptote of f (x) occurs at y = L if or
Def. A vertical asymptote of f (x) occurs at values of x where f (x) is undefined (sort of).
and are examples of graphs that have a hole.

7. Ex. Consider

8. One-Sided Limits
means that x approaches 2 from the right (larger than 2)
means that x approaches 2 from the left (smaller than 2)
Ex.

9. Thm.
The limit exists if both sides agree.

10. Ex. For the function given, find:

11. Ex. Find if

12. Def. (loose) A function is continuous on an interval if the graph has no gaps, jumps, or breaks on the interval.
Ex. Is continuous on [0,5]?

13. Def. (tight) A function f (x) is continuous on an interval if, for all points c on the interval:
exists

14. Ex. Let
Find a value of B so that f (x) is continuous at x = 0.