5. Consider Newton's method for solving the nonlinear equation f(x)=x²-a=0 where a > 0 whose two roots are √a. (a) Should the iterates {n} for satisfy 1 In÷1 (b) Let a = √a. Show that (In+a/xn). In 1-α = (n − a)²/(2x₂). (c) Suppose that To > 0. Show that for n ≥ 1, i. a < Int1 < In ii. In+1-α(Tn - α) iii. limno In = a.

5. Consider Newton's method for solving the nonlinear equation f(x)=x²-a=0 where a > 0 whose two roots are √a. (a) Should the iterates {n} for satisfy 1 In÷1 (b) Let a = √a. Show that (In+a/xn). In 1-α = (n − a)²/(2x₂). (c) Suppose that To > 0. Show that for n ≥ 1, i. a < Int1 < In ii. In+1-α(Tn - α) iii. limno In = a.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.1: Tables And Trends

Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...

See similar textbooks