## Transcribed Text

2. (Newton's Method of Computing the Square Root of a Positive
Number)
The equation x2 = a can be written in the form x = 1/2 (x + a/x). This
form leads to Newton's method
.
(a) Show that this difference equation has two equilibrium points, -va
and a.
(b) Sketch a stair step diagram for a ====== 3,x(0) = 1, and x(0) = -1.
(c) What can you conclude from (b)?
3. (Pielou's Logistic Equation)
E.C. Pielou [119] referred to the following equation as the discrete
logistic equation:
x(n+1)= = ax(n)
B > 0.
1 + Bx(n)
(a) Find the positive equilibrium point.
(b) Demonstrate, using the stair step diagram, that the positive equi-
librium point is asymptotically stable, taking a = 2 and B ======
1.
11. Suppose that the supply and demand equations are given by D(n) =
-2p(n) + 3 and S(n + 1) = p2(n)+1
(a) Assuming that the market price is the price at which supply equals
demand, find a difference equation that relates p(n + 1) to p(n).
(b) Find the positive equilibrium value of this equation.
(c) Use the stair step diagrams to determine the stability of the positive
equilibrium value.

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