# Is this going to be on the exam?

Recently there was a discussion on the AP Calculus Community bulletin board regarding whether it was necessary or desirable to have students do curve sketching starting with the equation and ending with a graph with all the appropriate features – increasing/decreasing, concavity, extreme values etc., etc. – included. As this is kind of question has…

# Visualizing Solid Figures 5

To end this series of posts on visualizing solid figures, we will look at a problem that relates to how volumes of solid figures are formed. It has 5 parts which will be presented first. Then the solution will be given. Consider the region in the first quadrant bounded by the graphs of the parabola…

# Visualizing Solid Figures 4

Volume by the method of “Cylindrical Shells” Today I will show you how to visualize the cylindrical shells used in computing the volume using Winplot. Winplot is a free program. Click here for Winplot and here for Winplot for Macs. For the example I will use the same situation as in the last post. This…