**Ch 1 - Limits & Continuity**

**Chapter 1 PDF Resource**

calculus_chapter_1.pdf |

**Lecture Notes & Videos**

Section 1-1

A Preview of Calculus

Notes on Simplifying a Complex Rational Expression and Rationalizing a Numerator

-----VIDEO: Simplifying a Complex Fraction using the LCD Method

Section 1-2 (Day 1)

Finding Limits Graphically, Numerically, and Analytically

-----VIDEO: A Brief Introduction to Limits

-----VIDEO: An Analytical Approach to Limits

-----VIDEO: Taking the Limit of Continuous Functions Using Direct Substitution

Section 1-2 (Day 2) and Section 1-3 (Day 1)

Epsilon-Delta Definition of a Limit and More on Limits

-----VIDEO: Epsilon-Delta Definition of a Limit

-----VIDEO: Common Mistake: The Limit of a Product is NOT ALWAYS EQUAL to the Product of the Limits

Section 1-3 (Day 2)

Taking the Limit of the Difference Quotient

-----VIDEO: Taking the Limit of the Difference Quotient

Section 1-3 (Day 3)

Limits of Trig Functions

-----VIDEO: Introduction to Trig Limits

-----VIDEO: Several Examples of Trig Limits

-----VIDEO: An Analytical Approach to Limits including Factoring, Rationalizing the Numerator, and Multiplying through by the LCD

-----YOUTUBE PLAYLIST: Individual Limit Problems Worked Out

Section 1-4 (Day 1)

Continuity

-----VIDEO: Definition of Continuity at a Point with 3 Counter-Examples

-----VIDEO: Taking the Limit of a Piecewise Function

-----VIDEO: AP Calculus AB FR Question: Continuity at a Point

Section 1-4 (Day 2)

Types of Discontinuity

-----VIDEO: Identifying Discontinuities by Type and Name

-----VIDEO: More on Discontinuity

Section 1-4 (Day 3)

Intermediate Value Theorem

-----VIDEO: Intermediate Value Theorem

Section 1-5 (Day 1)

Infinite Limits

Section 1-5 (Day 2)

More on Infinite Limits

Limits of Trig Functions

More Examples of Limits that involve Trig Functions

Limits Involving Square Roots

Another Example of a Limit using the Conjugate

-----VIDEO: A Commonly Missed Limit

A Preview of Calculus

Notes on Simplifying a Complex Rational Expression and Rationalizing a Numerator

-----VIDEO: Simplifying a Complex Fraction using the LCD Method

Section 1-2 (Day 1)

Finding Limits Graphically, Numerically, and Analytically

-----VIDEO: A Brief Introduction to Limits

-----VIDEO: An Analytical Approach to Limits

-----VIDEO: Taking the Limit of Continuous Functions Using Direct Substitution

Section 1-2 (Day 2) and Section 1-3 (Day 1)

Epsilon-Delta Definition of a Limit and More on Limits

-----VIDEO: Epsilon-Delta Definition of a Limit

-----VIDEO: Common Mistake: The Limit of a Product is NOT ALWAYS EQUAL to the Product of the Limits

Section 1-3 (Day 2)

Taking the Limit of the Difference Quotient

-----VIDEO: Taking the Limit of the Difference Quotient

Section 1-3 (Day 3)

Limits of Trig Functions

-----VIDEO: Introduction to Trig Limits

-----VIDEO: Several Examples of Trig Limits

-----VIDEO: An Analytical Approach to Limits including Factoring, Rationalizing the Numerator, and Multiplying through by the LCD

-----YOUTUBE PLAYLIST: Individual Limit Problems Worked Out

Section 1-4 (Day 1)

Continuity

-----VIDEO: Definition of Continuity at a Point with 3 Counter-Examples

-----VIDEO: Taking the Limit of a Piecewise Function

-----VIDEO: AP Calculus AB FR Question: Continuity at a Point

Section 1-4 (Day 2)

Types of Discontinuity

-----VIDEO: Identifying Discontinuities by Type and Name

-----VIDEO: More on Discontinuity

Section 1-4 (Day 3)

Intermediate Value Theorem

-----VIDEO: Intermediate Value Theorem

Section 1-5 (Day 1)

Infinite Limits

Section 1-5 (Day 2)

More on Infinite Limits

Limits of Trig Functions

More Examples of Limits that involve Trig Functions

Limits Involving Square Roots

Another Example of a Limit using the Conjugate

-----VIDEO: A Commonly Missed Limit

**Additional Handouts**

Notes on Asymptotes

Vertical Asymptotes & Unbounded Behavior

More Common Graphs to Memorize

Chapter 1 Theorems & Definitions

These theorems and definitions need to be memorized word for word.

Epsilon-Delta Definition of a Limit (Pictorial Representation)

Vertical Asymptotes & Unbounded Behavior

More Common Graphs to Memorize

Chapter 1 Theorems & Definitions

These theorems and definitions need to be memorized word for word.

Epsilon-Delta Definition of a Limit (Pictorial Representation)

**Practice Problems**

Finding Limits Graphically (w/KEY)

Approximating the Area Under a Curve (w/ KEY)

Epsilon-Delta Definition of a Limit (w/KEY)

More on the Epsilon-Delta Definition of a Limit (w/KEY)

Sketching Functions from a Set of Conditions (w/KEY)

More on Sketching Functions from a Set of Conditions (w/KEY)

Intermediate Value Theorem (w/KEY)

Practice with Trig Limits (w/KEY)

More Practice with Trig Limits (w/KEY)

Continuity at a Point (w/KEY)

Approximating the Area Under a Curve (w/ KEY)

Epsilon-Delta Definition of a Limit (w/KEY)

More on the Epsilon-Delta Definition of a Limit (w/KEY)

Sketching Functions from a Set of Conditions (w/KEY)

More on Sketching Functions from a Set of Conditions (w/KEY)

Intermediate Value Theorem (w/KEY)

Practice with Trig Limits (w/KEY)

More Practice with Trig Limits (w/KEY)

Continuity at a Point (w/KEY)

**Worksheets**

Rationalizing a Numerator WS

Simplifying a Complex Rational Expression WS

Taking the Limit of the Difference Quotient WS

Trig Review WS #1

Additional Practice on Limits & Continuity WS

More Practice on Limits & Continuity WS

Cumulative Review #1 - Chapter 1 WS

Cumulative Review #1 - Chapter 1 WS (w/ KEY)

Trig Limits WS

Trig Limits WS (w/ KEY)

Still More Practice on Limits & Continuity WS

Still More Practice on Limits & Continuity WS (w/ KEY)

Chapter 1 Review Concepts WS

Chapter 1 Review Concepts WS (w/ KEY)

Simplifying a Complex Rational Expression WS

Taking the Limit of the Difference Quotient WS

Trig Review WS #1

Additional Practice on Limits & Continuity WS

More Practice on Limits & Continuity WS

Cumulative Review #1 - Chapter 1 WS

Cumulative Review #1 - Chapter 1 WS (w/ KEY)

Trig Limits WS

Trig Limits WS (w/ KEY)

Still More Practice on Limits & Continuity WS

Still More Practice on Limits & Continuity WS (w/ KEY)

Chapter 1 Review Concepts WS

Chapter 1 Review Concepts WS (w/ KEY)

**Study Guides**

**(Used Prior to 2021-22)**

**Interactive Animations**

Calculus is the study of change. The ability to change a parameter and immediately see the result can demonstrate that change and how things are related during that change. Many of these concepts are much easier to explain if that change, the motion, can be visually demonstrated in class. Therefore, this is a perfect place for the use of computer animations.

All animations were created using the GeoGebra dynamic mathematics software application located on GeoGebra's website.

All animations were created using the GeoGebra dynamic mathematics software application located on GeoGebra's website.

**Please be patient! It takes awhile for these to load.**

Widen the browser, if necessary, to see the entire animation.

Widen the browser, if necessary, to see the entire animation.

**Area Under A Curve**

**A Secant Line Approaching a Tangent**