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: 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: 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
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
