Chapter 2 Videos

Section 2.1

  • Lesson 1: Where Do We Begin with Calculus, An Intro

    • Video

    • There are no formal guided notes for this lesson (refer to Blackboard for what to submit)

  • Examples: How to Find Average Value of a Function

  • Examples: How to Calculate the Slope at a Point and Find the Tangent Line (without limits or derivatives)

Section 2.2

  • Lesson 1: An Intro to the Idea of Limits and Calculating Basic Limits

  • Examples: Basic Limits

  • Lesson 2: Algebraic Tricks for Limits When You Get 0/0

  • Examples: Algebraic Tricks for Limits

  • Lesson 3: Limits that Do Not Exist

  • Lesson 4: The Sandwich Theorem (Squeeze Theorem) and Intro to Basic Trig Limits

  • Examples: Evaluating Basic Trig Limits

Section 2.4 (going out of order!)

  • Lesson 1: One-Sided Limits

  • Examples: One-Sided Limits - Basic Examples

  • Examples: One-Sided Limits - Absolute Value Examples

  • Lesson 2: Lim_(x->0) sin x/x = 1 Proof

  • Examples: How to Solve Limit Problems that Use lim_(x->0) sin x/x = 1

  • Step-by-Step Examples: Using lim_(x->0) sin x/x =1 if you’re still struggling

  • More Examples: How to Solve Limit Problems that Use lim_(x->0) sin x/x = 1

  • Examples: Troubleshooting Lim_(x->0) sin/x = 1 problems - common errors

Section 2.6

  • Lesson 1: A Quick Explanation of Limits as x->Inifinty or that Equal Infinity

  • Lesson 2: How to Evaluate Limits as x approaches infinity for Rational Functions

  • Review: How to do Polynomial Long Division / Finding Oblique Asymptotoes

  • Examples: Limits as x Approaches Infinity

  • Trickier Examples: Limits as x Approaches Infinity

  • Review: A Quick Review of All the Exponent Rules You Probably Forgot

  • Examples: Using the Conjugate Trick as x Approaches Infinity - A Comparison of Examples

  • Lesson 3: Horizontal Asymptotes and Limits at Infinity

  • Lesson 4: Limits that Equal Infinity

  • Examples: Limits that Equal Infinity

  • Lesson 5: Using Substitution with Some Tricky Limits Involving Infinity

  • Examples: Finding Horizontal / Vertical / Oblique Asymptotes

  • More Examples: Finding Horizontal / Vertical / Oblique Asymptotes

Section 2.3

  • Lesson 1: Understanding the Precise Definition of a Limit (you will need to memorize the definition)

  • Examples: When a Precise Epsilon is Given

  • Another Example: When a Precise Epsilon is Given, f(x)=1/x

  • Examples: When No Precise Epsilon is Given

Section 2.5

  • Lesson 1: An Intro to Continuity

  • Examples: Determining When Functions are Continuous

  • Examples: Finding Limits of Compositions of Continuous Functions

  • Lesson 2: The Intermediate Value Property and Continuity

  • Examples: Determining a Value that Will Make a Piecewise Function Continuous

  • Step-by-Step Examples: Determine a Value that Will Make Piecewise Functions Continuous (2 and 3 pieces)

  • Review: Piecewise Functions - a Review for Calc Students

Summary and Study Materials

  • Summary of Limits and Continuity: Everything reviewed in one video