Examples for Sections 12.1 and 12.2

Domain, Range Examples

Section 13.1 #18

DPGraph Picture of the Surface

Section 13.1 #20

DPGraph Picture of the Surface

Section 13.1 #22

DPGraph Picture1 of the Surface

Section 13.1 Pictures

Here are a variety of DPGraph views of the surface

Here is a DPGraph picture for Section 13.1 #48.

Here is a view of the same surface from the top. Look at z-slices.

Level Curve Example

Find the level curves for the given function and z-values of 11 and 27.

The level curves are shown below, 11 is shown in blue, 27 in red.

Click on the picture to see an animation showing 19 level curves ranging from z = 0 to z = 36.

Limit Example--Section 13.2 #32 (7e 24)

DPGraph Picture of the Surface

Take a look at this DPGraph picture of the cylinder y = -2x² and the surface given by

and think about the existence of

Click on the picture to see an animation.

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Lane Vosbury, Mathematics, Seminole State College email: vosburyl@seminolestate.edu