Limits, Asymptotes, and Continuity Ex.

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.

Ex. Find all asymptotes of, then sketch the graph.

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

Thm. The limit exists if both sides agree.

Ex. For the function given, find: a. b. c.

Ex. Find if

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]?

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

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