What are limits and how are they used in math?

Lesson #10Mini-Theme – “Limits”

The Eagles

Limit trivia – What band sang the song: “Take it to the Limit?”

Warm Up Follow Up: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 notationlim @ is called the “end behavior”

Value x approaches

Function or Graph to consider

What the function or graph approaches in terms of y

How do we read and define a limit?

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

Steve Prefontaine

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.”

Finding Limits on a Piecewise Function

Based on the piecewise function…

Find each of the below limits:

Where is the highest road speed limit in the world? 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.

CFU Follow UpHow do we define continuity on a graph? How do we prove that a graph lacks

continuity?