The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages.

Home Partial Differentiation Surfaces Examples Example 5: Hyperboloid of Two Sheets
 
del.icio.us Reddit Facebook StumbleUpon MySpace Twitter Search the VIAS Library  |  Index

Example 5: Hyperboloid of Two Sheets

Sketch the surface

11_partial_differentiation-34.gif

where

-2 ≤ z ≤ 2.

This is a hyperboloid of two sheets (Figure 11.1.17).

Although it is not a function, it can be broken up into two functions

11_partial_differentiation-40.gif

Step 1

Draw topographic maps for11_partial_differentiation-41.gifand The level curves are ellipses.11_partial_differentiation-42.gif

Step 2

Draw the axes and the planes z = 2, z = -2.

Step 3

Draw the intersections of the surface with the planes z = -2, z = 2, x = 0, y = 0. The surface intersects x = 0 and y = 0 in the hyperbolas

-(1/4)y2 + z2 = 1, -x2 + z2 = 1.

Step 4

Complete Figure 11.1.17.

11_partial_differentiation-39.gif

Figure 11.1.17
Home Partial Differentiation Surfaces Examples Example 5: Hyperboloid of Two Sheets

Last Update: 2006-11-15