4. Let f(x) = x* – 3x – 5. (a) Show that the equation f(x) = 0 has a unique root a in [1.5, 2]. (b) Let the iterative formula be x, = g(x,-1) = {/3x-1+5, for n = 1, 2, 3, .... 'n-1 'n-1 (i) Show that 1.5 < g(x)<2 for all x in [1.5, 2]. (ii) Find K= max g'(x) . 1.5Sxs2 (c) With x, = 2, find the least number of iterations required to give the estimate of a correct to %3D 4 decimal places and hence find the estimated value of a correct to 4 decimal places.
4. Let f(x) = x* – 3x – 5. (a) Show that the equation f(x) = 0 has a unique root a in [1.5, 2]. (b) Let the iterative formula be x, = g(x,-1) = {/3x-1+5, for n = 1, 2, 3, .... 'n-1 'n-1 (i) Show that 1.5 < g(x)<2 for all x in [1.5, 2]. (ii) Find K= max g'(x) . 1.5Sxs2 (c) With x, = 2, find the least number of iterations required to give the estimate of a correct to %3D 4 decimal places and hence find the estimated value of a correct to 4 decimal places.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.4: Complex And Rational Zeros Of Polynomials
Problem 15E
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![4. Let f(x) — х* — 3х-5.
(a) Show that the equation f(x) = 0 has a unique root a in [1.5, 2].
(b) Let the iterative formula be x, =g(x,-1)=
= /3x
+5, for n= 1, 2, 3, ....
n-1
(i) Show that 1.5 <g(x)<2 for all x in [1.5, 2].
(ii) Find K = max g'(x).
1.5<x<2
(c) With
= 2, find the least number of iterations required to give the estimate of a correct to
4 decimal places and hence find the estimated value of a correct to 4 decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F747a6fd0-fbea-40fb-a7e7-281eaf86de76%2F00ef46e8-4bde-4203-a8c4-17028f3c319f%2Fjr1513s_processed.png&w=3840&q=75)
Transcribed Image Text:4. Let f(x) — х* — 3х-5.
(a) Show that the equation f(x) = 0 has a unique root a in [1.5, 2].
(b) Let the iterative formula be x, =g(x,-1)=
= /3x
+5, for n= 1, 2, 3, ....
n-1
(i) Show that 1.5 <g(x)<2 for all x in [1.5, 2].
(ii) Find K = max g'(x).
1.5<x<2
(c) With
= 2, find the least number of iterations required to give the estimate of a correct to
4 decimal places and hence find the estimated value of a correct to 4 decimal places.
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