Daniel Kopsas

Newton's Method Examples

Implicit Differentiation Examples

Sketching a Rational Function Graph with a Hole

Derivative of 6x ln4x

Simple Limit Proof Using Epsilon-Delta Definition of a Limit

Continuity on an Interval

Domain of a Log Function

Function Language: Independent and Dependent Variable

Functions of Multiple Variables

Sketching a Rational Function Graph

Limits of Rational Functions That Do Not Simplify

Graphing a Piecewise-Defined Function

Systems of Three Linear Equations

Example: Average Value of a Function (Integrate by Substitution)

Example 1: Graphing a Function with Transformations

Rational Equations

Sketching a Polynomial Function Graph

Writing an Absolute Value as a Piecewise-Defined Function

Parent Root Functions

Proof of a Limit Value Using Epsilon and Delta

Graphing Transformed Exponential Functions

Identifying the Parent Function and Transformations

Graphing Absolute Value and Power Functions with Transformations

Introduction to Logarithms

Using Composition to Verify Two Functions are Inverses

Interval Notation

The Basic Secant Function Graph

Examples: End Behavior of a Polynomial Function

Completing the Square to Write the Equation of an Ellipse in Standard Form

Complex Numbers in Rectangular Form and Graphing

Dot Product and Angle Between 3D Vectors

Identifying the Parent Function and Transformations

Converting Photo to PDF Using PDFCreator

Rationalizing a Denominator with Two Terms Using the Conjugate

Counting Permutations with Duplicates

Sketching a Rational Function Graph with a Horizontal Asymptote

Differentiable Functions

Inverse Sine

Algebraic Limits: Absolute Value

The Argument of a Complex Number

The Mean Value Theorem for Integrals and the Average Value of a Function

Graphing Generic Functions with Transformations

Graphing a Linear Equation in Slope-Intercept Form

Transformations of Functions

Common Parent Functions

Factoring Refresher

Rational Functions with Oblique (Slant) Asymptotes

Calculating Mean, Median, Mode from Frequency Distribution

Optimization Example: Maximum and Minimum Vertical Distances Between Functions

Graphing a Transformed Cosine Function

Related Rates - Tip of Shadow