Important Terms and Concepts

  • Delta (δ)
  • Epsilon (ε )
  • Formal definition of limit
  • Indeterminate form
  • Removable discontinuity
  • One-sided limit
  • Intermediate value theorem
  • Image theorem
  • Step discontinuity
  • Undefined
  • Continuous
  • Vertical asymptote
  • Cusp
  • Piecewise function
  • Extreme value theorem

Learning Outcomes

In this chapter, students will...
  • Formalize the concept of a limit.
  • Learn the epsilon-delta definition of limit.
  • Apply the limit theorems.
  • Extend the concept of limits to cases involving infinity.
  • Apply the concepts of continuity and the intermediate value theorem.

Chapter 2 Sections

2-1 Numerical Approach to the Definition of Limit
Objective: Find the limits of ƒ(x) as a approaches c if ƒ(x) is undefined.
Homework: None
Aligned Instructional Resources: Khan Academy Video On the Concept of Limits

2-2 Graphical Approach to the Definition of Limit
Objective: Given a function ƒ, state whether or not ƒ(x) has a limit L as x approaches c, and if so, explain how close you must keep x to c in order for ƒ(x) to stay within a given number ε units of L
Homework: Q Problems 1-10, Problems 1-25 odd
Align Instructional Resources: Khan Academy Videos on Epsilon Delta Definition of Limits and YouTube Video on the Formal Definition of Derivative

2-3 The Limit Theorems
Objective: For the properties listed in the table in this section, be able to state them, use them in a proof, and explain why they are true 
Homework - Day 1: Q Problems 1-10, Problems 1-13 odd
Homework - Day 2: Problems 15-25 odd
Aligned Instructional Resources: YouTube Video of The Limit Theorems

2-4 Continuity and Discontinuity
Objective: Define continuity. Learn the definition by using it in several ways
Homework - Day 1: Q Problems 1-10, Problems 1-29 odd
Homework - Day 2: Problems 31-45 odd
Aligned Instructional Resources: Khan Academy Videos on Limits to Define Continuity

2-5 Limits Involving Infinity
Objective: Find limits of functions where either x becomes infinite or the limit is infinite
Homework: Q Problems 1-10, 1-13 odd, 12, 14
Aligned Instructional Resources: Khan Academy Videos on Limits and Infinity

2-6 The Intermediate Value Theorem and Its Consequences
Objectives: Given an equation for a continuous function
Homework - Day 1: Q Problems, 1-5 all
Homework - Day 2: 8-14 all
Aligned Instructional Resources: Khan Academy Video on the Mean Value Theorem