Outcomes
In this lesson you will learn
- limit notation
- the difference between right and left hand limits (one-sided limits)
- the slope of the tangent at a point
Students will be expected to:
- model real-world phenomena with a variety of functions/relations
- model real-world phenomena using polynomial functions and rational functions
- demonstrate an intuitive understanding of the concept of limit
- demonstrate an understanding for the conceptual foundations of limit, the area under a curve, the rate of change, and the slope of a tangent line, and their applications
- evaluate and apply limits
Introduction
By now you have been faced with many situations involving limits. This section however, introduces the concept of limit in the context of instantaneous rate of change. You have had an introduction to many of the concepts involved here in the Rate of Change unit in Mathematical Modeling, Book 3.
This section should require 1
to 2 hours to complete.
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- how to find the slope of a line
- average velocity
- secants and their slopes
- tangents and their slopes
- the concept of limit
- instantaneous rate of change
- how to use the TABLE feature on your graphing calculator