Maple Tutor

Part 13: The Error Function

The error function is an important function in the study of normally distributed data. In this part we will investigate this function while we practice elementary Maple commands.

1. Find an antiderivative of exp(-t^2). (Click here for help.)

   The function that appears erf is called the "error function." Let's see what we can find out about it.

2. Differentiate this function. (Click here for help.)

   Now evaluate the function at t = 0.(Click here for help.)

   Explain why these two calculations determine the error function completely.

3. Graph the derivative of the error function between t = -4 and t = 4. (Click here for help.)

   Is the derivative of the error function odd or even? How can you tell?

4. What is the total area under the graph of the derivative of the error function? (Click here for help. Note that Maple will allow plus and minus infinity as limits of integration.)

5. Look at the graph of the error function itself from t = -4 to t = 4. (Click here for help.)

   Is the error function even? odd? How can you tell?

6. Find the limit of erf(t) as t approaches infinity. (Click here for help.)

   How could you have determined this from the result in #4.