QuestionQuestion

Transcribed TextTranscribed 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.

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:
    Solution.zip.

    50% discount

    Hours
    Minutes
    Seconds
    $18.00 $9.00
    for this solution

    or FREE if you
    register a new account!

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Differential Equations Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Decision:
    Upload a file
    Continue without uploading

    SUBMIT YOUR HOMEWORK
    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats