Answered: 2 -0.5 0.5 1 1.5 2 -1

Math

Advanced Math

2 -0.5 0.5 1 1.5 2 -1

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.2: Exponents And Radicals

Problem 46E

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Question

Determine the roots of the following simultaneous nonlinear equations using (a) fixed-point iteration and (b) the Newton-Raphson method: y= x²+x+ 0.75 y+5xy = x² Employ initial guesses of x = y = 1.2 and discuss the results. Hints: The functions can be plotted (y versus x). The plot indicates that there are three real roots at about (-0.6, -0.18), (-0.19, 0.6), and (1.37, 0.24). -0.5 2 0.5 1 1.5 a) Put equations under these forms to solve and use x = y = 1.2 as initial guess: x=√x+0.75-y x² 1+5x b) Use the forms of u and v below to obtain the Jacobian. Use the same initial guess as in a). Iterate till & is close to 10-5 u(x, y) = x² + x + 0.75-y v(x, y) = x²-y-5xy