What are limits and how are they used in math?

1. What are limits and how are they used in math? Lesson #10 Mini-Theme – “Limits”

2. Limit trivia – What band sang the song: “Take it to the Limit?” The Eagles

3. Definition of a Limit: • This is what y approaches as x approaches or a specific number. • Write #9-10 from the warm up in limit notation • lim @ is called the “end behavior” What the function or graph approaches in terms of y Function or Graph to consider Value x approaches Warm Up Follow Up:

4. This limit is defined as the limit of the function f(x) as x approaches -3 from the LEFT • This limit is defined as the limit of the function y as x approaches 0 from the RIGHT How do we read and define a limit?

5. The movie based on this person’s life was called “Without Limits.” • This person once held every NCAA track record for all 7 track events from the 2000 meters to the 10,000 meters. • He was one of the first people to ever wear Nike shoes. • He is known for the quote: “To give less than your best is to sacrifice the gift.” Steve Prefontaine

6. Finding Limits on a Piecewise Function

7. Find each of the below limits: Based on the piecewise function…

8. The Autobahn in Germany has No Speed limit. (They do have an advisory speed limit of 81mph (130km/h)) Where is the highest road speed limit in the US? • Texas is currently testing an 85mph speed limit on a 41 mile stretch of road between Austin and Seguin. Where is the highest road speed limit in the world?

9. How do we define continuity on a graph? • How do we prove that a graph lacks continuity? CFU Follow Up