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


Example 1: Distance Between Two Points

Find the distance between P(7, 2) and Q(4, 6) (see Figure 1.1.7).

Δx = 4 - 7 = - 3, Δy = 6 - 2 = 4.

distance (P, Q) = 01_real_and_hyperreal_numbers-18.gif = 5.

We often deal with sets of points in the plane as well as on the line. One way to describe a set of points in the plane is by an equation or inequality in two variables, say x and y. A solution of an equation in x and y is a point (x0, y0) in the plane for which the equation is true. The set of all solutions is called the locus, or graph, of the equation. The circle is an important example of a set of points in the plane.

01_real_and_hyperreal_numbers-19.gif

Figure 1.1.7


Last Update: 2010-11-25