• #### Limits of Rational Functions - Problem 1

##### Math›Precalculus›Polynomial and Rational Functions
How to find the limit of a rational function as x goes to infinity (or negative infinity).
• #### Limits of Rational Functions - Problem 2

##### Math›Precalculus›Polynomial and Rational Functions
How to find the limit of a rational function (with quadratic polynomials) as x goes to negative infinity.
• #### Limits at a Glance - Problem 2

##### Math›Precalculus›Polynomial and Rational Functions
How to quickly find the limit of a rational function (cubic polynomials) as x goes to infinity.
• #### Continuity - Problem 2

##### Math›Calculus›Limits and Continuity
How to show that a function is discontinuous at a point x=a because the limit as x approaches a does not exist.
• #### Continuity - Problem 3

##### Math›Calculus›Limits and Continuity
How to show that a function is discontinuous at a point x=a because its limit and its value at x=a are different. Explanation of continuity.

• #### Continuity - Problem 1

##### Math›Calculus›Limits and Continuity
How to show that a function is discontinuous at a point x=a because it is not defined at a. Explanation of continuity.
• #### Continuous Functions - Problem 2

##### Math›Calculus›Limits and Continuity
How to show that rational functions are continuous functions.
• #### Continuous Functions - Problem 3

##### Math›Calculus›Limits and Continuity
How to show that compositions of continuous functions are continuous functions by checking continuity rules for the composition.
• #### Continuous Functions - Problem 1

##### Math›Calculus›Limits and Continuity
How to show that polynomial functions are continuous functions by checking the properties of continuous functions.
• #### The Definition of the Derivative - Problem 1

##### Math›Calculus›The Derivative
How to compute the derivative of a function at a point x=a using the definition of the derivative.
• #### The Definition of the Derivative - Problem 2

##### Math›Calculus›The Derivative
How to estimate the derivative of a function at a point x=a.
• #### The Derivative Function - Problem 1

##### Math›Calculus›The Derivative
How to use the definition of the derivative to find a formula for the derivative function.
• #### Average Value of a Function - Problem 3

##### Math›Calculus›The Definite Integral
How to find the average value of a function over an interval [a,b].
• #### The Definition of the Derivative - Problem 3

##### Math›Calculus›The Derivative
How to compute the derivative using the definition, and how to find an equation of the line tangent to its graph at a point.
• #### The Definite Integral - Problem 1

##### Math›Calculus›The Definite Integral
How to use geometry to find the definite integral.
• #### The Definite Integral - Problem 3

##### Math›Calculus›The Definite Integral
How to approximate a definite integral with rectangular sums.
• #### The Definite Integral - Problem 2

##### Math›Calculus›The Definite Integral
How to evaluate a definite integral that involves a parabola.
• #### Average Value of a Function - Problem 1

##### Math›Calculus›The Definite Integral
How to find the average value of a function over an interval [a,b].
• #### Computing Definite Integrals using Substitution - Problem 1

##### Math›Calculus›The Definite Integral
How to evaluate definite integrals using the method of substitution.