Introduction and Limits

L.0 - Introduction

Objectives

• • Explain what differentiation is

  • Explain what integration is

  • Introduce the concept of the limit

Activities

• 1. Introduction Video - In this video I introduce the idea of the derivative and integral

  2. Reading 2.1 from openstax Calculus vol. 1

L.1 - Limits

Objectives

• • Define limit and write limits with proper notation

  • Determine the value of a limit at a point

  • Use a graphing calculator to graph functions and create tables to evaluate a function

  • Recognize when a limit does not exist

  • Relate vertical asymptotes and inifite limits

  • Find left and right handed limits

Activities

• • Video L1A - In this video I give a definition of limit and explain how to use a graph and table to find the value of a limit.

  • Video L1B - In this video I give examples of when Limits do not exist and introduce left and right handed limits.

  • Video L1C - In this video I introduce infinite limits and relate them to vertical asymptotes.  I also work through an example problem finding limits using a graph.

  • Reading 2.2 - This is the section covered in the videos.  Read through it and work a few of the example problems

  • Suggested problems

    • 2.2 Section Review: 38, 39, 41, 46-49, 50-54

    • Number 38  worked on a calculator - This shows how to set up the table on a TI-84 so you can input values into the table

L.2 - The Limit Laws

Objectives

• • Recognize the basic limit laws.

  • Use the limit laws to evaluate the limit of a function.

  • Evaluate the limit of a function by factoring.

  • Use the limit laws to evaluate the limit of a polynomial or rational function.

  • Evaluate the limit of a function by factoring or by using conjugates.

Activities

• • Video L2A - The Limit Laws - This video covers the basic limit laws covering the arithmetic of limits

  • Video L2B - Evaluating Limits in simple cases

  • Video L2C - Finding the limit by factoring and multiplying by the conjugate

  • Video L2D - Finding limits by simplifying

  • Reading 2.3 The Limit Laws - Don't worry about the limits of trig functions or the squeeze theorem. The discussion on one sided limits and limits that take on the from K/0 is worth reading, it readdresses infinite limits.

    • Practice Problems from the end of section 2.3:   87-89, 91, 93-97, 101, 102